Section 10  Partial Differential Equations

Section 10: Partial Differential Equations

Invited Lectures

Wednesday, 19 August  H 1012

16:15 – 17:00 Fabrice Bethuel, Université Paris-Sud, Orsay, France Recent results for Ginzburg-Landau models (I: p.121) Chair: Dmitri Yafaev

17:15 – 18:00 Robert R. Jensen, Loyola University of Chicago, Chicago, USA Viscosity solutions of elliptic partial differential equations (I: p.122) Chair: Stefan Müller

Thursday, 20 August  H 1012

14:00 – 14:45 Matei Machedon, University of Maryland, College Park, USA Fourier Analysis of Null Forms and Non-linear Wave Equations (I: p.124) Chair: Michael Struwe

15:00 – 15:45 Frank Eric Merle, Université de Cergy-Pontoise, Cergy-Pontoise, France Blow-up Phenomenon For Critical Nonlinear Schrödinger and Zakharov Equations (I: p.124) Chair: Elmar Schrohe

Friday, 21 August  H 1012

16:15 – 17:00 Gustavo Alberto Ponce, University of California, Santa Barbara, USA On nonlinear dispersive equations (I: p.125) Chair: Mikhail Shubin

17:15 – 18:00 Frédéric Hélein, CMLA, ENS-Cachan, Cachan, France Phenomena of compensation and estimates for partial differential equations (I: p.121) Chair: Gunther A. Uhlmann

Saturday, 22 August  H 1012

16:15 – 17:00 Gunther A. Uhlmann, University of Washington, Seattle, USA Inverse Boundary Value Problems for Partial Differential Equations (I: p.127) Chair: Bert-Wolfgang Schulze

17:15 – 18:00 Mikhail Vasilevich Safonov, University of Minnesota, Minneapolis, USA Estimates near the boundary for solutions of second order parabolic equations (I: p.126) Chair: Heinz O. Cordes

Monday, 24 August  H 1012

14:00 – 14:45 Dmitri Yafaev, Université Rennes-1, Rennes, France Scattering theory: some old and new problems (I: p.127) Chair: Volker Enß

15:00 – 15:45 Hans Lindblad, University of California at San Diego, La Jolla, USA Minimal regularity solutions of nonlinear wave equations (I: p.122) Chair: Konrad Gröger

Partial Differential Equations  Section 10

Short Communications and Poster Sessions

Short Communications  Wednesday, 19 August
General Theory  H 111

Chair: Massimo Lanza de Cristoforis

14:00 – 14:15 Wenxiong Chen, Southwest Missouri State Univ., Springfield, MO, USA High Order Conformally Invariant Equations (p.200)

14:15 – 14:30 Paweł Domański, A. Mickiewicz University, Fac. of Mathematics & Comp. Sci., Poznań, Poland Splitting of differential complexes (p.201)

14:30 – 14:45 Massimo Lanza de Cristoforis, Università di Padova, Padova, Italy Differentiability Properties of the Autonomous Composition Operator in Sobolev Spaces (p.213)

Elliptic Equations I  H 110

Chair: Florin C. Muscalu

14:00 – 14:15 Evgeni A. Kalita, Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine New class of a priori estimates for nonlinear elliptic equations and systems of high order (p.208)

14:15 – 14:30 Vladimir A. Kondratiev, Moscow State University, Moscow, Russia On Properties of Positive Solutions of Elliptic Equations (p.210)

14:30 – 14:45 Florin C. Muscalu, Brown University, Providence, Rhode Island, USA A Harnack Type Theorem for Elliptic Systems with L^{∞} Coefficients (p.214)

A Priori Estimates & Asymptotics  H 111

Chair: Shuji Watanabe

15:00 – 15:15 Sergey Frolovitchev, MTUCI, Moscow, Russia Multiplicative solution asymptotics for Kolmogorov-Feller equation and asymptotics of the boundary value problems (p.203)

15:15 – 15:30 Annegret Glitzky, WIAS, Berlin, Germany Electro–reaction–diffusion systems in heterostructures (p.204)

15:30 – 15:45 Shuji Watanabe, Toyota National College of Technology, Toyota-shi, Japan An embedding theorem of Sobolev type related to a generalized Fourier transform and applications to partial differential equations with singularity (p.224)

Applied Fluids  H 110

Chair: Lizabeth V. Rachele

15:00 – 15:15 Olaf Schmidtmann, WIAS Berlin, Berlin, Germany Stability Problems in Turbo Compressors (p.220)

15:15 – 15:30 Lizabeth V. Rachele, Purdue University, West Lafayette, IN, USA Inverse Problems for Elastic Media (p.218)

Short Communications  Thursday, 20 August
Systems I  H 111

Chair: Yakov Krasnov

16:15 – 16:30 Gennadii V. Demidenko, Sobolev Institute of Mathematics, Novosibirsk, Russia Systems not of Cauchy–Kovalevskaya type (p.201)

16:30 – 16:45 Abduhamid Dzhuraev, Tajik Academy of Siences, Dushanbe, Tadschikistan On partial differential equations in the unit ball of ℂ^{n}, which are singular at the origin and on the boundary (p.202)

16:45 – 17:00 Yakov Krasnov, Bar-Ilan University, Ramat-Gan, Israel Symmetries of Cauchy-Riemann-Füter Equation (p.211)

Fluids  H 111

Chair: Mitsuo Morimoto

17:15 – 17:30 Song Jiang, Institute of Applied Physics and Computational Math., Beijing, P.R. China Large-time behavior of solutions to the equations of a one-dimensional viscous polytropic ideal gas in unbounded domains (p.207)

17:30 – 17:45 Anatoli Merzon, Moscow State Pedagogical University, Moscow, Russia A complete solution of the Ursell problem (p.213)

17:45 – 18:00 Hiroko Morimoto, Meiji University, Kawasaki-City, Japan On the Existence of Steady Navier-Stokes Flow in 2D Tube-like Domain under General Outflow Condition (p.214)

Short Communications  Friday, 21 August
Elliptic Equations II (Singularities & Index Theory)  H 111

Chair: Vladimir S. Rabinovich

14:00 – 14:15 Vladimir Borisovich Vasil’ev, Novgorod State University, Novgorod, Russia Wave factorization of elliptic symbols (p.223)

14:15 – 14:30 Igor I. Skrypnik, Institute of Applied Mathematics and Mechanics NASU, Donetsk, Ukraine Degree of densely defined (S)_{+} operators and applications (p.222)

14:30 – 14:45 Vladimir S. Rabinovich, Rostov State University, Rostov-na-Donu, Russia Elliptic boundary value problems in domains with non-Lipschitz singular points (p.218)

Hyperbolic Equations I (Integrable Equations)  H 110

Chair: Jiahong Wu

14:00 – 14:15 Igor Anders, Institute for Low Temperature Physics & Engineering, Kharkov, Ukraine Long-time asymptotic behaviour of non-decaying solutions of KP-type equations (p.198)

14:15 – 14:30 Tariel Kiguradze, Tbilisi I. Javakhishvili State University, Tbilisi, Georgia On periodic solutions of nonlinear second order hyperbolic equations (p.209)

14:30 – 14:45 Jiahong Wu, University of Texas at Austin, Austin, USA Zero dissipation limits of wave equations (p.225)

PDE and Mathematical Physics  H 111

Chair: Roland Potthast

15:00 – 15:15 Johannes Elschner, WIAS Berlin, Berlin, Germany Existence, uniqueness, and regularity for solutions of the conical diffraction problem (p.203)

15:15 – 15:30 Frank Jochmann, Humboldt–Universität Berlin, Berlin, Germany Existence and asymptotic behavior of weak solutions of the drift diffusion equations for semiconductors (p.207)

15:30 – 15:45 Roland Potthast, University of Göttingen, Göttingen, Germany On mixed reciprocity relations in inverse scattering (p.217)

Navier-Stokes Equations  H 110

Chair: Takeyuki Nagasawa

15:00 – 15:15 Mikhail E. Bogovskii, Friendship of Nations University of Russia, Moscow, Russia The problem of global smooth solutions for multidimensional Navier-Stokes equations solved (p.199)

15:15 – 15:30 Soichiro Katayama, Wakayama University, Wakayama, Japan Some semilinear wave equations with nonlinear damping terms (p.208)

15:30 – 15:45 Takeyuki Nagasawa, Tohoku University, Sendai, Japan A new energy inequality and partial regularity for weak solutions of Navier-Stokes equations (p.215)

Short Communications  Saturday, 22 August
Elliptic Equations III (Spectral Theory)  H 111

Chair: Tetsutaro T. Shibata

14:00 – 14:15 Gabriella Bognár, University of Miskolc, Miskolc, Hungary On a nonlinear eigenvalue problem (p.198)

14:15 – 14:30 Jochen Denzler, Technische Universität München, München, Germany Existence of windows with minimal heat diffusion (p.201)

14:30 – 14:45 Tetsutaro T. Shibata, Hiroshima University, Higashi-Hiroshima, Japan Asymptotic behavior of eigenvalues of nonlinear elliptic two-parameter problems (p.221)

Systems II  H 110

Chair: Joachim Naumann

14:00 – 14:15 Hakop A. Hakopian, Gdansk University, Gdansk, Poland On two partial differential and one algebraic systems (p.205)

14:15 – 14:30 Waichiro Matsumoto, Université de Paris 6, Paris, France On the Cauchy-Kowalevskaya theorem of Nagumo type for systems (p.213)

14:30 – 14:45 Joachim Naumann, Humboldt–Universität Berlin, Berlin, Germany Interior Hölder continuity of weak solutions to nonlinear parabolic systems in two spatial dimensions (p.215)

Hyperbolic Equations II (Shocks, Blow-up, and Other Singular Phenomena)  H 111

Chair: Ya-Guang Wang

15:00 – 15:15 Mehmet Can, Istanbul Technical University, Istanbul, Turkiye Blow up of solutions of a quasilinear hyperbolic equation with applications (p.199)

15:15 – 15:30 Michael Ruzicka, Inst. of Applied Mathematics, University Bonn, Bonn, Germany Electrorheological fluids, an example for systems with non-standard growth (p.219)

15:30 – 15:45 Ya-Guang Wang, Shanghai Jiao Tong University, Shanghai, P.R. of China Nonlinear Geometrical Optics for Shock Waves (p.224)

Diffusion Processes  H 110

Chair: Natalia I. Grinberg

15:00 – 15:15 Jack Carr, Heriot-Watt University, Edinburgh, Scotland Asymptotic Behaviour of Solutions to a simplified Lifshitz-Slyozov Equation (p.200)

15:15 – 15:30 Alexander M. Chebotarev, Moscow State University, Moscow, Russia Resolvent theory for quantum dynamical semigroup (p.200)

15:30 – 15:45 Natalia I. Grinberg, Universität Münster, Münster, Germany Inverse boundary problem for 2D diffusion equation (p.205)

Short Communications  Monday, 24 August
Elliptic Equations IV (Non-linear Problems)  H 111

Chair: Hwai-Chiuan Wang

16:15 – 16:30 Carsten Ebmeyer, Universität Bonn, Bonn, Germany The p-Laplacian under mixed boundary value conditions in multidimensional polyhedral domains

(p.203)

16:30 – 16:45 Stanislav I. Pohozaev, Steklov Mathematical Institute, Moscow, Russia Positive solutions of nonlinear Neumann problems. Application of the global fibering method

(p.217)

16:45 – 17:00 Hwai-Chiuan Wang, Tsing Hua University, Hsinchu, China, Taiwan Semilinear Elliptic Problems in Interior and Exterior Flask Domains (p.224)

Applied Problems I  H 110

Chair: Olga S. Rozanova

16:15 – 16:30 Zhiming Chen, Academia Sinica, Beijing, China, Peoples Republic of Adaptive Finite Element Methods for Dynamical GL Vortices in Superconductivity (p.200)

16:30 – 16:45 Olga S. Rozanova, Belgorod State University, Belgorod, Russia 2-D model of atmosphere dynamics: energy balance and some properties of solutions (p.219)

16:45 – 17:00 Gregory A. Chechkin, Moscow State University, Mech & Math, Moscow, Russia On Behavior of Perforated Bodies with Rapidly Oscillating Surfaces

Hyperbolic Equations III (Conservation Laws & Asymptotic Behavior)  H 111

Chair: Armen Shirikyan

17:15 – 17:30 Christian Klingenberg, Universität Würzburg, Würzburg, Germany Conservation laws with source terms (p.209)

17:30 – 17:45 Andrzej Rogowski, University of Łódź, Łódź, Poland Existence of space periodic solutions for semi-linear hyperbolic systems (p.218)

17:45 – 18:00 Armen Shirikyan, Moscow State University, Moscow, Russia Asymptotic behaviour of solutions to second-order hyperbolic equations (p.221)

Reaction-Diffusion Equations  H 110

Chair: Klaus Zacharias

17:15 – 17:30 Gideon A. Ngwa, University of Buea, Buea, Cameroon The Effects of Boundary Conditions on Reaction Diffusion Equations (p.216)

17:30 – 17:45 Arnd Scheel, FU Berlin, FB Mathematik, Berlin, Germany Essential instability of pulses amd bifurcations to modulated travelling waves (p.220)

17:45 – 18:00 Klaus Zacharias, Weierstraß Institute, Berlin, Germany On a reaction–diffusion system modelling chemotaxis (p.225)

Short Communications  Tuesday, 25 August
Elliptic Equations V (Fourier and Harmonic Analysis)  H 111

Chair: Pawel Strzelecki

16:15 – 16:30 Alip Mohammed, FB Mathematik und Informatik, FU-Berlin, Berlin, Germany Riemann problem related to the Shilov boundary (p.214)

16:30 – 16:45 Dian K. Palagachev, University of Chemical Technology and Metallurgy, Sofia, Bulgaria Oblique derivative problem for uniformly elliptic operators with VMO coefficients and applications

(p.216)

16:45 – 17:00 Paweł Strzelecki, Warsaw University, Warsaw, Poland Regularity for subelliptic p-harmonic maps and the ghost of Hardy spaces (p.222)

Parabolic Equations  H 111

Chair: Nicolay Draganov Kutev

17:15 – 17:30 Helmut Koch, Humboldt–Universität, Berlin, Germany Large time regularity of solutions to the porous medium equation (p.210)

17:30 – 17:45 Bernd Kawohl, Universität Köln, Köln, Germany Image processing and anisotropic diffusion (p.208)

17:45 – 18:00 Nicolay Draganov Kutev, Mathematisches Institut, Köln, Germany Maximum and comparison principle for anisotropic diffusion (p.212)

Short Communications  Wednesday, 26 August
PDE and Dynamical Systems  H 111

Chair: Alexandre Kometch

14:00 – 14:15 Andrey Yu. Goritsky, Moscow State University, Moscow, Russia Integral manifolds with exponential tracking (p.204)

14:15 – 14:30 Jörg Härterich, FU Berlin, Berlin, Germany Heteroclinic Orbits Between Rotating Waves in Hyperbolic Balance Laws (p.205)

14:30 – 14:45 Alexandre Kometch, Moscow State University, Moscow, Russia Attractors for Hamiltonian Nonlinear Wave Equations (p.210)

Non-linear Theory  H 110

Chair: Masafumi Yoshino

14:00 – 14:15 Vladimir Kozlov, University of Linköping, Linköping, Sweden Singularities of solutions of nonlinear elliptic equations (p.211)

14:15 – 14:30 Sidi Mohammed Bouguima, University of Tlemcen, Tlemcen, Algeria Free boundary problem in the plane (p.199)

14:30 – 14:45 Masafumi Yoshino, Chuo University, Tokyo, Japan Global solvability of fully nonlinear equations and Toeplitz operators (p.225)

Hyperbolic Equations IV (General Theory)  H 111

Chair: Pavel A. Krutitskii

15:00 – 15:15 Ludmila S. Pulkina, Samara State University, Samara, Russia A nonlocal problem for the hyperbolic equation (p.217)

15:15 – 15:30 Peetta Kandy Ratnakumar, Indian Statistical Institute, Bangalore, India Wave Equation for the Hermite Operator (p.218)

15:30 – 15:45 Pavel A. Krutitskii, Moscow State University, Moscow, Russia Initial-boundary value problems in multiply connected domains for an equation of composite type

(p.212)

Applied Problems II (Elasticity & Fusion)  H 110

Chair: Juan Francisco Padial

15:00 – 15:15 Alexander A. Kosmodemyanskii, MIIT Dept. of Comp. Math., Moscow, Russia On the location of fail points in Torsion Problem (p.211)

15:15 – 15:30 Juan Francisco Padial, Universidad Politécnica de Madrid, Madrid, Spain Some mathematical models related to nuclear fusion (p.216)

Poster Session  Tuesday, 25 August 14:00 – 15:45  MA 144

Faina S. Berezovskaya, Center of Forest Ecology, Moscow, Russia

About solutions Ltraveling waves of Lienard equation cross-diffusion updatings (p.198) Roland Duduchava, A. Razmadze Mathematical Institute, Tbilisi, Georgia

Asymptotics of solutions to crack–type and mixed problems (p.202) Atsuhiko Eida, Tokyo Engineering University, Tokyo, Japan

Harmonic Analysis of Functions (p.203) Kenji Hasegawa, Kongakuin University, Tokyo, Japan

Boundedness of Pseudodifferential Operators (p.206) Toshio Horiuchi, Ibaraki University, Mito, Japan

Removable singularities for quasilinear degenerate elliptic equations with absorption terms (p.206) Jaan Janno, Institute of Cybernetics, Tallinn, Estonia

Inverse problems for determining weakly singular kernels in partial integrodifferential equations (p.207) Akisato Kubo, Fujita Health University, Toyoake, Aichi, Japan

Global existence of a classical solution to □u − μu + au^{m} = 0 (p.212) Tokumori Nanbu, Toyama Medical and Pharmaceutical University, Toyama, Japan

On solutions of some nonlinear degenerate parabolic equations (p.215) Dmitry Shepelsky, Seoul National University, Seoul, Korea

Inverse problem for a stratified uniaxial bianisotropic medium (p.220)

Yuming Shi, ENS-Cachan, Cachan, France

A Foias-Saut type of expansion for a dissipative wave equation (p.221) Georgi V. Smirnov, Universidade de Évora, Evora, Portugal

A Periodic Knitting Problem for the Helmholtz Equation (p.222) Anna Surkova, Institute for Low Temperature Physics, Kharkov, Ukraine

On the localization of the surface states for some class of the discrete Schrödinger oparators with surface potential Kiyoshi Takeuchi, Hiroshima University, Hiroshima, Japan

Higher-codimensional boundary value problems for D-modules (p.222) Jan Turo, Technical University of Gdansk, Gdansk, Poland

Solution of first order stochastic functional partial differential equations via integral contractors (p.223) Leonid Volevich, Keldysh Institute of Applied Mathematics, Moscow, Russia

Stable and unstable manifolds for elliptic equations with parameter (p.223)