Proceedings Of The 4th European Conference Elliptic And Parabolic Problems

This book provides an overview of the state of the art in important subjects, including — besides elliptic and parabolic issues — geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis. Contents:Rolduc:Models for Shape Memory Alloys Described by Subdifferentials of Indicator Functions (T Aiki & N Kenmochi)Local Stability Under Changes of Boundary Conditions at a Far Away Location (M Chipot & A Rougirel)Existence of Solutions of a Segregation Model Arising in Population Dynamics (G Galiano et al.)Global Attractors for Multivalued Flows Associated with Subdifferentials (N Kenmochi & N Yamazaki)Quasiconvexity and Optimal Design (P Pedregal)A Comparison Principle for the p-Laplacian (A Poliakovsky & I Shafrir)Gaeta:Nonlinear Diffusion in Irregular Domains (U G Abdulla)Viscosity Lyapunov Functions for Almost Sure Stability of Degenerate Diffusions (M Bardi & A Cesaroni)Approximating Exterior Flows by Flows on Truncated Exterior Domains: Piecewise Polygonal Artificial Boundaries (P Deuring)Epidemic Models with Compartmental Diffusion (W E Fitzgibbon et al.)Exact Controllability of Piezoelectric Shells (B Miara)Bifurcation in Population Dynamics (K Umezu)and other papers Readership: Graduate students and researchers in the fields of partial differential equations and applied mathematics. Keywords:

This book provides an overview of the state of the art in important subjects, including ? besides elliptic and parabolic issues ? geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis.

This book provides an overview of the state of the art in important subjects, including - besides elliptic and parabolic issues - geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis. Contents: Rolduc: Models for Shape Memory Alloys Described by Subdifferentials of Indicator Functions (T Aiki & N Kenmochi); Local Stability Under Changes of Boundary Conditions at a Far Away Location (M Chipot & A Rougirel); Existence of Solutions of a Segregation Model Arising in Population Dynamics (G.

The conference Challenges In Scientific Computing (CISC 2002) took place from October, 2 to 5, 2002. The hosting institution was the Weierstrass Insti tute for Applied Analysis and Stochastics (WIAS) in Berlin, Germany. The main purpose of this meeting was to draw together researchers working in the fields of numerical analysis and scientific computing with a common interest in the numerical treatment and the computational solution of systems of nonlinear partial differential equations arising from applications of physical and engineering problems. The main focus of the conference was on the problem class of non linear transport/diffusion/reaction systems, chief amongst these being: the Navier-Stokes equations, semiconductor-device equations and porous media flow problems. The emphasis was on unsolved problems, challenging open questions from applications and assessing the various numerical methods used to handle them, rather than concentrate on accurate results from "solved" problems. Thanks to the participants it was an interesting meeting. The presentations stimulated exchanging ideas and lively discussions. This proceedings comprises 13 papers form the conference, ranging from numerical methods for flow problems, multigrid methods, semiconductor and microwave simulation, solution methods, finite element analysis to software aspects. This interesting conference would not have been possible without the help of the staff of the WIAS. I thank all participants, and all our supporters, especially those not onstage, for making the conference a success.

This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.

This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics including equations and systems of elliptic and parabolic type and various applications in physics, mechanics and engineering. These topics are now part of various areas of science and have experienced tremendous development during the last decades. -------------------------------------

The book is an account on recent advances in elliptic and parabolic problems and related equations, including general quasi-linear equations, variational structures, Bose-Einstein condensate, Chern–Simons model, geometric shell theory and stability in fluids. It presents very up-to-date research on central issues of these problems such as maximal regularity, bubbling, blowing-up, bifurcation of solutions and wave interaction. The contributors are well known leading mathematicians and prominent young researchers. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Maximal Regularity and Quasilinear Parabolic Boundary Value Problems (H Amann)Remarks on the Two and Three Membranes Problem (J-F Rodrigues et al.)Bubbling and Criticality in Two and Higher Dimensions (M del Pino & M Musso)Blow Up Solutions for a Liouville Equation with Singular Data (P Esposito)Problems in Unbounded Cylindrical Domains (P Guidotti)Entire Solutions of Some Reaction-Diffusion on Equations (J-S Guo)Some Abelian Gauge Field Theories in the Self-dual and Nonself-dual Cases (J Han & N Kim)Ginzburg–Landau Equations on Non-uniform Media (S Kosugi)Finding the Elasticae by Means of Geometric Gradient Flows (C-C Lin & H R Schwetlick)Free Work Identity and Nonlinear Instability in Fluids with Free Boundaries (M Padula)Complete and Energy Blow-up in Superlinear Parabolic Problems (P Quittner)Non-stabilizing Solutions for a Supercritical Semilinear Parabolic Equation (E Yanagida)and other papers Readership: Graduate students and researchers in partial differential equations and mathematical physics. Keywords:Elliptic Equations;Parabolic Problems;Nonlinear Analysis;Partial Differential EquationsKey Features:Presents up-to-date research in many important and hot topicsWritten by first class researchers in related fieldsContains rich models arising from different fields