modelling and analysis of problems in continuum … · 3rd workshop of the gamm activity group...

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3rd Workshop of the GAMM Activity GroupAnalysis of Partial Differential Equations

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University of Kassel, September 30 - October 2, 2015

Modelling and Analysis of Problems in Continuum Mechanics

http://www.uni-kassel.de/go/gamm-pde2015

U N I V E R S I T .A. T SG E S E L L S C H A F T K A S S E L e.V.

GESELLSCHAFT fürANGEWANDTE MATHEMATIK und MECHANIK e.V.INTERNATIONAL ASSOCIATION of APPLIED MATHEMATICS and MECHANICS

⚫ Program

⚫ Abstracts

⚫ Participants

3rd Workshop of the GAMM Activity Group Analysis ofPartial Differential Equations

Modelling and Analysis

of Problems in Continuum Mechanics

University of Kassel, September 30 – October 2, 2015

Organizers

Dorothee Knees · Maria Specovius-Neugebauer

Local Organizing Committee

C. Franke · D. Knees · M. Specovius-Neugebauer · A. Stylianou

The workshop is supported by: Universitätsgesellschaft Kassel e.V.

3rd Workshop of the GAMM Activity Group Analysis of PDEsUniversity of Kassel, September 30 – October 2, 2015 Program

Wednesday, 30.09.2015, 14:00 - 18:00

13:30 - 14:00 Registration14:00 - 14:10 Opening14:10 - 14:55 Phase Transitions in a Nonlocal Fokker-Planck Equation

Niethammer, Barbara14:55 - 15:40 Singular and jump-discontinuous patterns in reaction-diffusion-ode models

Marciniak-Czochra, Anna15:40 - 16:10 Coffee break16:10 - 16:55 Creating a spectral gap through inverse spectral theory

Chirilus-Bruckner, Martina17:00 - 17:30 Smoothness of 1D fractional Keller-Segel system with critical and supercritical

diffusionBurczak, Jan

17:30 - 18:00 Analysis of p()-Laplace thermistor models for electrothermal feedback in organicsemiconductor devicesGlitzky, Annegret

Thursday, 01.10.2015, 09:00 - 17:30

09:00 - 09:45 Improved fractional differentiability for elastic plastic deformation with hardeningwith boundary behaviourFrehse, Jens

09:45 - 09:50 Short break09:50 - 10:35 Limiting strain models in elasticity theory and variational integrals with linear

growthBulicek, Miroslav

10:35 - 11:05 Coffee break11:05 - 11:35 Stochastic Homogenization of Prandtl-Reuss Plasticity

Heida, Martin11:35 - 12:05 Damage processes in thermoviscoelastic materials with damage-dependent ther-

mal expansion coefficientsHeinemann, Christian

12:05 - 12:35 A posteriori modelling error estimates for the assumption of perfect incompress-ibility in the Navier-Stokes equationFischer, Julian

12:35 - 14:00 Lunch Break14:00 - 14:45 Mathematical challenges arising in the analysis of chemotaxis-fluid interaction

Winkler, Michael14:45 - 14:50 Short break14:50 - 15:20 On the problem of singular limit in a Navier-Stokes-Fourier model coupled with the

transport of radiative intensityNecasová, Sárka

15:20 - 16:00 Coffee break16:00 - 17:30 Activity Group Meeting19:00 - ... Brauhaus Zum Rammelsberg, Rammelsbergstraße 4, 34131 Kassel–Bad Wil-

helmshöheDinner

Program3rd Workshop of the GAMM Activity Group Analysis of PDEs


Friday, 02.10.2015, 09:00 - 12:20

09:00 - 09:45 Flow of micromagnetic complex fluidsBenesová, Barbora

09:45 - 09:50 Short break09:50 - 10:20 From adhesive contact to brittle delamination in visco-elastodynamics

Thomas, Marita10:20 - 10:50 Coffee break10:50 - 11:20 EDP-convergence and the limit from diffusion to reaction

Mielke, Alexander11:20 - 11:25 Short break11:25 - 12:10 Long time asymptotics for non-convex gradient flows

Matthes, Daniel12:10 - 12:20 Closing

The Workshop Dinner will take place at 19:00 on Thursday, at

Brauhaus Zum RammelsbergRammelsbergstraße 434131 Kassel–Bad Wilhelmshöhewww.zum-rammelsberg.de

3rd Workshop of the GAMM Activity Group Analysis of PDEsUniversity of Kassel, September 30 – October 2, 2015 Abstracts

List of Abstracts

Abstracts3rd Workshop of the GAMM Activity Group Analysis of PDEs


Invited talk

Flow of micromagnetic complex fluids

Benesová, BarboraUniversität Würzburg, Institut für Mathematik

Campus Hubland Nord, Emil-Fischer-Straße 40, 97074, Würzburg, Germany.email: [email protected]

In the talk, we will present a model for micromagnetic fluids. Such flu-ids have many technological applications. They can not only be found inmedical applications, but also in loud speakers and shock absorbers.

We investigate micromagnetic material in the framework of complex flu-ids. The system of PDEs to model the flow of the material is derived in acontinuum mechanical setting with the help of variational techniques. Weoutline the process of modelling and the energetic variational approach.Moreover, we highlight the coupling between the elastic and the magneticproperties of the material.

Since the entire model is rather complex we obtain a first simplified ver-sion to analyse. We also have an explicit solution of the magnetization intwo dimensions which leads to special equations and existence analysis onweak solutions is done.

This is joint work with Carlos García-Cervera (Mathematics Department,University of California, Santa Barbara, USA), Johannes Forster, AnjaSchlömerkemper (Institute for Mathematics, University of Würzburg, Ger-many), and Chun Liu (Department of Mathematics, Penn State University,University Park, USA).


Invited talk

Limiting strain models in elasticity theory and variationalintegrals with linear growth

Bulicek, MiroslavCharles University, School of Mathematics,

Sokolovská 83, 186 75 Praha 8, Czech Republic.email: [email protected]

We investigate the properties of certain elliptic systems leading, a priori,to solutions that belong to the space of Radon measures. We show that if theproblem is equipped with a so-called Uhlenbeck structure, then the solutioncan in fact be understood as a standard weak solution, with one proviso:analogously as in the case of minimal surface equations, the attainment ofthe boundary value is penalized by a measure supported on (a subset of) theboundary, which, for the problems under consideration here, is the part ofthe boundary where a Neumann boundary condition is imposed. Finally, wewill connect such elliptic systems with certain problems in elasticity theory–the limiting strain models.

This is the joint work with Lisa Beck, Josef Málek and Endre Süli.



Contributed talk

Smoothness of 1D fractional Keller-Segel system withcritical and supercritical diffusion

Burczak, JanPolish Academy of Sciences, Institute of Mathematics,

ul. Sniadeckich 8, 00-656, Warsaw, Poland.email: [email protected]

There is a strong evidence, both theoretical and experimental, that feed-ing strategies based on isotropic α-stable Lévy processes (generated by(−Δ)

α2 ) are both closer to optimal than Brownian motion (generated by

−Δ) and indeed used by certain organisms, especially in low-prey-densityconditions. Hence it is justified to consider the fractional (parabolic-elliptic)Keller-Segel equations:

(1)t + (−Δ)

α2 = −χdiv (∇),

−Δ = − ⟨⟩.Let us focus on the case of one space dimension D = 1. Then problem (1)has global-in-time, regular solutions for α > 1 as well as α = 1 with smalldata. Blowups occur for α < 1 – see [1], [5] and [2]. Consequently, the caseα = 1 seemed critical: thus in [1] the authors conjecture a blowup for largedata.

In my talk I will show that in fact the opposite claim holds and that, havingadded to (1)1 logistic damping r(1 − ), the solutions are smooth also inthe supercritical regime α > mx(1 − r/χ,0). This is joint work with RafaelGranero-Belinchon (Davis), see [3, 4].

References

[1] Bournaveas, N., Calvez. V., The one-dimensional Keller-Segel model with fractional dif-fusion of cells, Nonlinearity, 23(4):923, 2010.

[2] Burczak, J., Granero-Belinchón, R., Boundedness of large-time solutions to a chemo-taxis model with nonlocal and semilinear flux, to appear in Topological Methods in Non-linear Analysis, for a preliminary version, see arxiv preprint arXiv:1409.8102 [math.AP].

[3] Burczak, J., Granero-Belinchón, R., Keller-Segel meets Burgers on S1, submitted, for apreliminary version, see arxiv preprint arXiv:1504.00955 [math.AP].

[4] Burczak, J., Granero-Belinchón, R., Global solutions for a supercritical drift-diffusionequation, submitted, for a preliminary version, see arxiv preprint arXiv:1507.00694[math.AP].

[5] Escudero., C., The fractional Keller-Segel model, Nonlinearity, 19(12), 2006, 2909 –2918.


Invited talk

Creating a spectral gap through inverse spectral theory

Chirilus-Bruckner, MartinaUniversity of Leiden, Mathematical Institute,

Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands.email: [email protected]

The analysis of existence, stability and bifurcations of solutions to dynam-ical systems can be simplified through the use of center manifold theory, ameans of a reducing the dimension of the problem. In particular, for partialdifferential equations, which can be viewed as infinite-dimensional dynami-cal systems, such a reduction is of particular interest, but is often inhibiteddue to the absence of a spectral gap. We explain how center manifold theorycan be applied to non-autonomous problems in which, at first sight, such anendeavour seems hopeless due to the “generic” absence of a spectral gap,but a reduction becomes possible after solving an inverse spectral problem.In other words, we demonstrate that the infinitely many parameters inher-ent in non-autonomous coefficients can be used to overcome difficulties thatare out of reach in the autonomous case. We illustrate the successful use ofthis strategy along a range of problems whose common theme is the searchof time-periodic solutions in the setting of dispersive equations with spatiallyperiodic coefficients. This is joint work with Gene Wayne.



Contributed talk

A posteriori modelling error estimates for the assumption ofperfect incompressibility in the Navier-Stokes equation

Fischer, JulianUniversität Leipzig, Max Planck Institute for Mathematics in the Sciences,

Konstantinstr. 15, 04315, Leipzig, Germany.email: [email protected]

Considering a slightly compressible fluid, we derive guaranteed a poste-riori estimates for the difference between an approximate solution to theincompressible Navier-Stokes equation and any corresponding weak solu-tion to the compressible Navier-Stokes equation (in the sense of P.-L. Lions).We do not assume any additional regularity of solutions to the compressibleNavier-Stokes equation, but work with just the known regularity of weak so-lutions as constructed by Lions. All constants in our estimates are explicit.Heuristics suggest that our estimates for the modelling error are of optimalorder in case of well-behaved flows and divergence-free approximations ofthe velocity field.


Invited talk

Improved fractional differentiability for elastic plasticdeformation with hardening with boundary behaviour

Frehse, JensUniversität Bonn–Hausdorff Center for Mathematics, Institute of Applied Mathematics

Endenicher Allee 60, 53115, Bonn, Germany.email: [email protected]



Contributed talk

Analysis of p(x)-Laplace thermistor models forelectrothermal feedback in organic semiconductor devices

Glitzky, AnnegretWeierstrass Institute for Applied Analysis and Stochastics,

Mohrenstraße 39, 10117, Berlin, Germany.email: [email protected]

Organic semiconductor devices are thin-film multilayer structures basedon organic molecules or polymers. Their mobility laws contain strong pos-itive feedback w.r.t. temperature, density and field strength. Such devicesare increasingly used as photovoltaic cells, organic transistors, and triodes.In addition to displays, organic LEDs also occur in intelligent lighting appli-cations. In large-area organic LEDs spatially inhomogeneous luminance athigh power due to inhomogeneous current flow and electrothermal feedbackcan be observed, see [1].

To describe these self-heating effects in organic semiconductors we pre-sent a stationary thermistor model featuring non-Ohmic current-voltage lawsand self-heating effects, see [3]. The coupled system consists of the current-flow equation for the electrostatic potential and the heat equation with Jouleheating term as source. The self-heating in the device is modelled by anArrhenius-like temperature dependency of the electrical conductivity. Thenon-Ohmic electrical behaviour is described by a power law such that theelectrical conductivity depends nonlinearly on the electric field. Notably, weallow for functional substructures with different power laws, which gives riseto a p()-Laplace-type problem with piecewise constant exponent.

We prove the existence and boundedness of solutions in the two-dimen-sional case. The crucial point is to establish the higher integrability of thegradient of the electrostatic potential to tackle the Joule heating term. Theproof of the improved regularity is based on Caccioppoli-type estimates,Poincaré inequalities, and a Gehring-type Lemma for the p()-Laplacian. Fi-nally, Schauder’s fixed-point theorem is used to show the existence of solu-tions, for details see [2].

The talk presents joint work with Matthias Liero and Thomas Koprucki(WIAS) and reports on experimental results of Axel Fischer and ReinhardScholz (Institute of Applied Photophysics, TU Dresden).

References

[1] A. Fischer, T. Koprucki, K. Gärtner, M. L. Tietze, J. Brückner, B. Lüssem, K. Leo, A. Glitzky,and R. Scholz, Feel the heat: Nonlinear electrothermal feedback in organic LEDs, Adv.Funct. Mater. 24 (2014), no. 22, 3366–3366.

[2] A. Glitzky and M. Liero, Analysis of p()-Laplace thermistor models describing the elec-trothermal behavior of organic semiconductor devices, Preprint 2143, Weierstraß-Institutfür Angewandte Analysis und Stochastik, Berlin, 2015.

[3] M. Liero, T. Koprucki, A. Fischer, R. Scholz, and A. Glitzky, p-Laplace thermistor modelingof electrothermal feedback in organic semiconductors, Preprint 2082, Weierstraß-Institutfür Angewandte Analysis und Stochastik, Berlin, 2015, to appear in Z. Angew. Math.Phys., DOI 10.1007/s00033-015-0560-8.


Contributed talk

Stochastic Homogenization of Prandtl-Reuss Plasticity

Heida, MartinWeierstrass Institute for Applied Analysis and Stochastics,


We consider the Prandtl-Reuss model of infinitesimal strain plasticity inthe quasistatic regime. Assuming kinematic hardening, we analyse the ho-mogenization of the system in the case that coefficient functions (includingthe convex function that describes the flow rule) are heterogeneous with asmall parameter ϵ. In particular, the heterogeneous structure is assumedto be given through a stationary and ergodic dynamical system scaled byϵ. We are interested in an effective law that describes limits of solutions asϵ→ 0. We obtain the effective system using the recently developed needle-problem approach to homogenization.



Contributed talk

Damage processes in thermoviscoelastic materials withdamage-dependent thermal expansion coefficients

Heinemann, ChristianWeierstrass Institute for Applied Analysis and Stochastics,


This talk is devoted to an evolutionary system which models damage pro-cesses in viscoelastic media coupled with heat conduction. The novelty ofthe system under consideration is that the thermal expansion coefficient isallowed to depend on the damage phase field variable. This dependence re-sults in additional nonlinear coupling terms entering the system. We presenta suitable discretization scheme, a series of a priori estimates and a globalin time existence result for weak solutions.

The talk is based on a joint work with Elisabetta Rocca (WIAS Berlin).


Invited talk

Singular and jump-discontinuous patterns inreaction-diffusion-ode models

Marciniak-Czochra, AnnaUniversität Heidelberg, Institute of Applied MathematicsIm Neuenheimer Feld 294, 69120, Heidelberg, Germany.

email: [email protected]

In this talk we explore mechanisms of pattern formation arising in pro-cesses described by a system of a single reaction-diffusion equation coupledto ordinary differential equations. Such systems of equations arise, for ex-ample, in modelling of interactions between cellular processes and diffusinggrowth factors. Our theory applies to a wide class of pattern formation mod-els with an autocatalytic non-diffusing component. We show that the lackof diffusion in some model components may lead to instability of all regularstationary patterns and emergence of stable patterns with jump discontinu-ity or of singular spike patters.

Investigation of such structures pose challenges for mathematical analy-sis as well as numerical simulation and visualisation of the model solutions.We discuss analytical and numerical aspects of the proposed models as wellas interpret the results in context of biomedical applications. Moreover, wefind a class of reaction-diffusion-ode models with DDI-induced blow-up ofspatially heterogeneous solutions.



Invited talk

Long time asymptotics for non-convex gradient flows

Matthes, DanielTechnische Universität München, Zentrum Mathematik,

Boltzmannstraße 3, 85747, München, Germany.email: [email protected]

In this talk, I will discuss the long time behaviour of two gradient flows: thefirst (joint work with R.McCann and G.Savare) is the fourth order degenerateparabolic Hele-Shaw equation, that is related to the rupture of thin fluidfilms, and whose solutions become self-similar eventually. The second flow(joint work with J.Zinsl) is a variant of the parabolic-parabolic Keller-Segelsystem modelling the aggregation of bacteria, which eventually reach a non-trivial equilibrium state.

The Hele-Shaw equation is the gradient flow of the Dirichlet energy withrespect to the Wasserstein distance, the Keller-Segel system is a gradientflow for a combination of entropy and energy terms in a joint Wasserstein-L2-metric. Neither of the two potentials is geodesically λ-convex in the re-spective metric, so the long time asymptotics do not come for free from thevariational structure.

The key observation is that each of the two models possesses an auxiliaryLyapunov functional that is intimately related to the flow and the metricstructure. A precise control on the auxiliary dissipation also controls thelong time behaviour.


Contributed talk

EDP-convergence and the limit from diffusion to reaction

Mielke, AlexanderWeierstrass Institute for Applied Analysis and Stochastics,


We discuss evolutionary -convergence of gradient systems based on DeGiorgi’s energy-dissipation principle (EDP). We apply this method to passto the limit from a pure diffusion equation with a suitably scaled high en-ergy barrier to a reaction-diffusion system, which is then given in terms ofa generalized gradient system. (This is joint work with Matthias Liero, MarkPeletier, and Michiel Renger.)



Contributed talk

On the problem of singular limit in a Navier-Stokes-Fouriermodel coupled with the transport of radiative intensity*

Necasová, SárkaAcademy of Sciences of the Czech Republic, Dep. of Evol. Equations,

Zitna 25, 11567, Prague, Czech Republic.email: [email protected]

*Joint work with Bernard Ducomet (CEA, France), [email protected]

We consider relativistic and “semi-relativistic” models of radiative viscouscompressible Navier-Stokes-Fourier system coupled to the radiative transferequation extending the classical model introduced in [1] and we study someof its singular limits (low Mach and diffusion) in the case of well-preparedinitial data and Dirichlet boundary condition for the velocity field. In thelow Mach number case we prove the convergence toward the incompress-ible Navier-Stokes system coupled to a system of two stationary transportequations. In the diffusion case we prove the convergence toward the com-pressible Navier-Stokes with modified state functions (equilibrium case) ortoward the compressible Navier-Stokes coupled to a diffusion equation (nonequilibrium case). Moreover, the coupling with magnetic field and singularlimit will be described.

References

[1] B. Ducomet, E. Feireisl, S. Necasová: On a model of radiation hydrodynamics. Ann. I. H.Poincaré-AN 28 (2011) 797–812.

[2] B. Ducomet, S. Necasová: Low Mach number limit in a model of radiative flow, Journalof Evolution equations, 14 (2014) 357–385.

[3] B. Ducomet, S. Necasová: Diffusion limits in a model of radiative flow, Ann. Univ. FerraraSez. VII Sci. Mat. 61 (2015), no. 1, 17–59.

[4] B. Ducomet, S. Necasová: Singular limits in a model of radiative flow, J. Math. FluidMech. 17 (2015), 2, 341–380.

[5] B. Ducomet, S. Necasová: Non-relativistic limit in a model of radiative flow. Analysis(Berlin) 35 (2015), no. 2, 117–137.


Invited talk

Phase Transitions in a Nonlocal Fokker-Planck Equation

Niethammer, BarbaraUniversität Bonn–Hausdorff Center for Mathematics, Institute of Applied Mathematics,

Endenicher Allee 60, 53115 Bonn, Germany.email: [email protected]

We discuss a nonlocal Fokker-Planck equation that describes energy min-imisation in a double well-potential and is driven by a time-dependent con-straint. Via formal asymptotic analysis we identify different small parame-ter regimes that correspond to hysteretic and non-hysteretic phase transi-tions respectively. For the fast reaction regime that is related to Kramers-type phase transitions we also indicate how can rigorously derive a rate-independent evolution equation in a small parameter limit.

This is joint work with Michael Herrmann and Juan Velazquez.



Contributed talk

From adhesive contact to brittle delamination invisco-elastodynamics

Thomas, MaritaWeierstrass Institute for Applied Analysis and Stochastics,


This contribution addresses two models describing the rate-independentfracture of a material compound along a prescribed interface in a visco-elastic material. This unidirectional process is modeled in the frameworkof Generalized Standard Materials with the aid of an internal delaminationparameter. In the context of (fully) rate-independent systems within theenergetic formulation it has become a well-established procedure to obtainsolutions of the brittle model via an adhesive-contact approximation basedon tools of evolutionary Gamma-convergence. This means that the non-smooth, local brittle constraint, confining displacement jumps to the nullset of the delamination parameter, is approximated by a smooth, non-localsurface energy term. Here, we discuss the extension of this approach forsystems that couple the rate independent evolution of the delamination pa-rameter with a viscous and dynamic evolution of the displacements in thebulk. This is joint work with Riccarda Rossi (Brecia).


Invited talk

Mathematical challenges arising in the analysis ofchemotaxis-fluid interaction

Winkler, MichaelUniversität Paderborn, Institut für Mathematik,

Warburger Str. 100, 33098, Paderborn, Germany.email: [email protected]

We consider models for the spatio-temporal evolution of populations ofmicro-organisms, moving in an incompressible fluid, which are able to par-tially orient their motion along gradients of a chemical signal. Accordingto modelling approaches accounting for the mutual interaction of the swim-ming cells and the surrounding fluid, we study study parabolic chemotaxissystems coupled to the (Navier-)Stokes equations through transport andbuoyancy-induced forces.

The presentation discusses mathematical challenges encountered evenin the context of basic issues such as questions concerning global existenceand boundedness, and attempts to illustrate this by reviewing some recentdevelopments. A particular focus will be on strategies toward achieving apriori estimates which provide information sufficient not only for the con-struction of solutions, but also for some qualitative analysis.

3rd Workshop of the GAMM Activity Group Analysis of PDEsUniversity of Kassel, September 30 – October 2, 2015 Participants

List of Participants

Participants3rd Workshop of the GAMM Activity Group Analysis of PDEs



Abels, Helmut Prof. Dr.Universität RegensburgFakultät für MathematikUniversitätsstr. 3193053 Regensburg, [email protected]

Bartocha, Damian Dipl.-Math.Universität KasselInstitut für MathematikHeinrich-Plett-Str. 4034132 Kassel, [email protected]

Benesová, Barbora Dr.Universität WürzburgInstitut für MathematikCampus Hubland NordEmil-Fischer-Straße 4097074 Würzburg, [email protected]

Bulicek, Miroslav Prof.Charles UniversitySchool of MathematicsSokolovská 83186 75 Praha 8, Czech [email protected]

Burczak, Jan Dr.Polish Academy of SciencesInstitute of Mathematicsul. Sniadeckich 800-656 Warsaw, [email protected]

Chirilus-Bruckner, Martina Prof.University of LeidenMathematical InstituteNiels Bohrweg 12333 CA Leiden, The [email protected]

Denk, Robert Prof. Dr.Universität KonstanzUniversitätsstraße 1078464 Konstanz, [email protected]



Disser, Karoline Dr.Weierstrass Institute for Applied Analysisand StochasticsMohrenstraße 3910117 Berlin, [email protected]

Düll, Wolf-Patrick PD Dr.Universität StuttgartInstitut für Analysis, Dynamik und ModellierungPfaffenwaldring 5770569 Stuttgart, [email protected]

Fischer, Julian Dr.Universität LeipzigMax Planck Institute for Mathematics in the SciencesKonstantinstr. 1504315 Leipzig, [email protected]

Frehse, Jens Prof.Universität Bonn–Hausdorff Center for MathematicsInstitute of Applied MathematicsEndenicher Alle 6053115 Bonn, [email protected]

Gilg, Steffen Dipl.-Math.Universität StuttgartInstitut für Analysis, Dynamik und ModellierungPfaffenwaldring 5770569 Stuttgart, [email protected]

Glitzky, Annegret PD Dr.Weierstrass Institute for Applied Analysisand StochasticsMohrenstraße 3910117 Berlin, [email protected]

Gößwein, Michael MSc.Universität RegensburgFakultät für MathematikGraduiertenkolleg 1692Universitätsstr. 3193053 Regensburg, [email protected]


Haas, Tobias Dipl.-Math.Universität StuttgartInstitut für Analysis, Dynamik und ModellierungPfaffenwaldring 5770569 Stuttgart, [email protected]

Heida, Martin Dr.Weierstrass Institute for Applied Analysisand StochasticsMohrenstraße 3910117 Berlin, [email protected]

Heinemann, Christian Dr.Weierstrass Institute for Applied Analysisand StochasticsMohrenstraße 3910117 Berlin, [email protected]

Kierkels, Arthur H.M. MSc.Universität BonnInstitute of Applied MathematicsEndenicher Allee 6053115 Bonn, [email protected]

Knees, Dorothee Prof. Dr.Universität KasselInstitut für MathematikHeinrich-Plett-Str. 4034132 Kassel, [email protected]

Luo, Yongming MSc.Universität KasselInstitut für MathematikHeinrich-Plett-Str. 4034132 Kassel, [email protected]

Marciniak-Czochra, Anna Prof. Dr.Universität HeidelbergInstitute of Applied MathematicsIm Neuenheimer Feld 29469120 Heidelberg, [email protected]



Matthes, Daniel Prof. Dr. habil.Technische Universität MünchenZentrum MathematikBoltzmannstraße 385747 München, [email protected]

Mielke, Alexander Prof. Dr.Weierstrass Institute for Applied Analysisand StochasticsFG Partielle DifferentialgleichungenMohrenstraße 3910117 Berlin, [email protected]

Necasová, Sárka Prof.Academy of Sciences of the Czech RepublicDep. of Evol. EquationsZitna 2511567 Prague, Czech [email protected]

Niethammer, Barbara Prof. Dr.Universität Bonn–Hausdorff Center for MathematicsInstitute of Applied MathematicsEndenicher Allee 6053115 Bonn, [email protected]

Schlömerkemper, Anja Prof. Dr.Universität WürzburgInstitut für MathematikCampus Hubland NordEmil-Fischer-Straße 4097074 Würzburg, [email protected]

Schneider, Guido Prof. Dr.Universität StuttgartInstitut für Analysis, Dynamik und ModellierungPfaffenwaldring 5770569 Stuttgart, [email protected]

Seis, Christian Dr.Universität BonnInstitute of Applied MathematicsEndenicher Allee 6053115 Bonn, [email protected]


Specovius-Neugebauer,Maria

Prof. Dr.

Universität KasselInstitut für MathematikHeinrich-Plett-Str. 4034132 Kassel, [email protected]

Stylianou, Athanasios Dr.Universität KasselInstitut für MathematikHeinrich-Plett-Str. 4034132 Kassel, [email protected]

Thomas, Marita Dr.Weierstrass Institute for Applied Analysisand StochasticsMohrenstraße 3910117 Berlin, [email protected]

Winkler, Michael Prof. Dr.Universität PaderbornInstitut für MathematikWarburger Str. 10033098 Paderborn, [email protected]

Zanger, Florian Dr.Universität DüsseldorfMathematisches InstitutUniversitätsstr. 1, Gebäude 25.1340225 Düsseldorf, [email protected]

Zimmermann, Dominik Dr.Universität StuttgartInstitut für Analysis, Dynamik und ModellierungPfaffenwaldring 5770569 Stuttgart, [email protected]

For Your Notes3rd Workshop of the GAMM Activity Group Analysis of PDEs


3rd Workshop of the GAMM Activity Group Analysis of PDEsUniversity of Kassel, September 30 – October 2, 2015 For Your Notes

For Your Notes3rd Workshop of the GAMM Activity Group Analysis of PDEs


modelling and analysis of problems in continuum … · 3rd workshop of the gamm activity group...

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