Recent Advances on Elliptic And Parabolic Issues: Proceedings of the 2004 Swiss-japanese Seminar, Zurich, Switzerland, 6-10 December 2004

by Chipot, Michel

• ISBN13: 9789812566751
• ISBN10: 9812566759
• Format: Hardcover
• Copyright: 2006-04-30
• Publisher: World Scientific Pub Co Inc

Summary

This volume is a collection of articles discussing the most recent advances on various topics in partial differential equations. Many important issues regarding evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completeness of the articles will make this book a source of inspiration and references in the future. Contents: Steady Free Convection in a Bounded and Saturated Porous Medium (S Akesbi et al.); Quasilinear Parabolic Functional Evolution Equations (H Amann); A Linear Parabolic Problem with Non-Dissipative Dynamical Boundary Conditions (C Bandle & W Reichel); Remarks on Some Class of Nonlocal Elliptic Problems (M Chipot); On Some Definitions and Properties of Generalized Convex Sets Arising in the Calculus of Variations (B Dacorogna et al.); Note on the Asymptotic Behavior of Solutions to an Anisotropic Crystalline Curvature Flow (C Hirota et al.); A Reaction-Diffusion Approximation to a Cross-Diffusion System (M Iida et al.); Bifurcation Diagrams to an Elliptic Equation Involving the Critical Sobolev Exponent with the Robin Condition (Y Kabeya); Ginzburg-Landau Functional in a Thin Loop and Local Minimizers (S Kosugi & Y Morita); Singular Limit for Some Reaction Diffusion System (K Nakashima); Rayleigh-Benard Convection in a Rectangular Domain (T Ogawa & T Okuda); Some Convergence Results for Elliptic Problems with Periodic Data (Y Xie); On Global Unbounded Solutions for a Semilinear Parabolic Equation (E Yanagida). Key Features An accessible presentation of the latest, cutting-edge topics in partial differential equations Written by leading scholars in related fields Readership: Graduate students and researchers in partial differential equations and nonlinear science.

Table of Contents

Preface	v
Samir Akesbi, Bernard Brighi, and Jean-David Hoernel
Steady free convection in a bounded and saturated porous medium	1	(18)
Herbert Amann
Quasilinear parabolic functional evolution equations	19	(26)
Catherine Bandle, Wolfgang Reichel
A linear parabolic problem with non-dissipative dynamical boundary conditions	45	(34)
Michel Chipot
Remarks on some class of nonlocal elliptic problems	79	(24)
Bernard Dacorogna, Ana Margarida Ribeiro
On some definitions and properties of generalized convex sets arising in the calculus of variations	103	(26)
Chiaki Hirota, Tetsuya Ishiwata, Shigetoshi Yazaki
Note on the asymptotic behavior of solutions to an anisotropic crystalline curvature flow	129	(16)
Masato Lida, Hirokazu Ninomiya
A Reaction-Diffusion Approximation to a Cross-Diffusion System	145	(20)
Yoshitsugu Kabeya
Bifurcation diagrams to an elliptic equation involving the critical Sobolev exponent with the Robin condition	165	(26)
Satoshi Kosugi, Yoshihisa Morita
Ginzburg—Landau functional in a thin loop and local minimizers	191	(28)
Kimie Nakashima
Singular limit for some reaction diffusion system	219	(22)
Toshiyuki Ogawa, Takashi Okuda
Rayleigh-Benard convection in a rectangular domain	241	(24)
Y. Xie
Some convergence results for elliptic problems with periodic data	265	(18)
Eiji Yanagida
On global unbounded solutions for a semilinear parabolic equation	283