Reaction Diffusion Systems

"Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."

Preface

iii

(4)

Contributors

vii

Symmetry and Nonsymmetry in Some Overdetermined Boundary Value Problems

1

(12)

Giovanni Alessandrini

R. Magnanini

Asymptotical Behavior of Solutions of Some Reaction-Diffusion Systems

13

(8)

Marie-Francoise Bidaut-Veron

Nonlinear Singular Parabolic Equations

21

(16)

Piotr Biler

Tadeusz Nadzieja

Andrzej Raczynski

Nonlinear Liouville Theorems

37

(14)

Isabeau Birindelli

Existence and Regularity Results for Quasilinear Parabolic Equations

51

(8)

Lucio Boccardo

Elliptic Systems with Various Growth

59

(8)

Lucio Boccardo

Jacqueline Fleckinger-Pelle

Francois de Thelin

Some Uniqueness Results for XXXu+f(u) = O in R(N), N Greater than Equal to 3

67

(12)

Carmen Cortazar

Manuel Elgueta

Patricio Felmer

A Strong Comparison Principle for the Dirichlet p-Laplacian

79

(10)

Mabel Cuesta

Peter Takac

Geometric Properties of Solutions to Subelliptic Equations in Nilpotent Lie Groups

89

(18)

Donatella Danielli

Nicola Garofalo

Recent Progress on Super-Diffusive Nonlinear Parabolic Problems

107

(14)

Panagiota Daskalopoulos

Manuel A. del Pino

On Linear Perturbations of Superquadratic Elliptic Systems

121

(10)

Djairo G. de Figueiredo

M. Ramos

An Age Dependent Regularization of Martin's Problem

131

(10)

William E. Fitzgibbon

J.J. Morgan

M.E. Parrott

G.F. Webb

Uniqueness and Positivity for Solutions of Equations with the p-Laplacian

141

(16)

Jacqueline Fleckinger-Pelle

Jesus Hernandez

Peter Takac

Francois de Thelin

On the First Curve in the Fucik Spectrum of a Mixed Problem

157

(6)

Jean-Pierre Gossez

A. Marcos

The Maximum Principle and Positive Principal Eigenfunctions for Polyharmonic Equations

163

(20)

Hans-Christoph Grunau

Guido Sweers

Positive Solutions for the Logistic Equation with Unbounded Weights

183

(16)

Jesus Hernandez

Recent Results on Selfsimilar Solutions of Degenerate Nonlinear Diffusion Equations

199

(18)

Josephus Hulshof

Optimal L(XXX) and Schauder Estimates for Elliptic and Parabolic Operators with Unbounded Coefficients

217

(24)

Alessandra Lunardi

Vincenzo Vespri

The Quasi-Isothermal Limit in Porous Catalysts

241

(14)

Francisco J. Mancebo

Jose M. Vega

On the Reaction-Diffusion Electrolysis Nonlinear Elliptic Equations

255

(34)

Stanislav Pohozaev

Existence of Nonnegative Solutions for Generalized p-Laplacians

289

(10)

Humberto Prado

Pedro Ubilla

Stability and Blow-Up for Dissipative Evolution Equations

299

(20)

Patrizia Pucci

James Serrin

A Nonlinear Schrodinger Equation Defined on the Whole Space

319

(16)

Ian Schindler

Asymptotic Behavior for Large Time of Solutions of Nonlinear Evolution Equations with Dissipation

335

(14)

Ilia A. Shishmarev

Hardy's Inequality for the Stokes Problem

349

(16)

Pavel E. Sobolevskii

Semilinear Biharmonic Problems on R(N)

365

(12)

Nikos Stavrakakis

Magnetic Field Wave Equations for TM-Modes in Nonlinear Optical Waveguides

377

(24)

Charles Stuart

On the Behavior of Positive Solutions for a Class of Semilinear Elliptic Systems

401

Cecilia Yarur

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Reaction Diffusion Systems

Summary

Table of Contents

Supplemental Materials