Nonlinear Partial Differential Equations and Their Applications

College de France Seminar Volume XIV

Doina Cioranescu, Jaques-Louis Lions

• Publisher: North Holland
• Year: 2002
• Print ISBN: 9780444511034
• eBook ISBN: 9780080537672
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Dedication
• Preface
• Chapter 1: An Introduction to Critical Points for Intergral Functionals
• Chapter 2: A Semigroup Formulation for Electrmagnetic Waves in Dispersive Dielectric Media
• Chapter 3: Limite Non Visqueuse Pour Les Fluides Incompressibles Axisymetriques
• Chapter 4: Global Properties of Some Nonlinear Parabolic Equations
• Chapter 5: A model for two coupled turbulent fluids part I: Analysis of the system
• Chapter 6: Determination de Conditions Aux Limites En Mer Ouverte Par Une Methode de Controle Optimal
• Chapter 7: Effective diffusion in vanishing viscosity
• Chapter 8: Vibration of a Thin Plate With a “Rough” Surface
• Chapter 9: Anisotropy and Dispersion in Rotating Fluids
• Chapter 10: Integral equations and saddle point formulation for scattering problems
• Chapter 11: Existence and uniqueness of a strong solution for nonhomogeneous micropolar fluids
• Chapter 12: Homogenization of dirichlet minimum problems with conductor type periodically distributed constraints
• Chapter 13: Transport of trapped particles in a surface potential
• Chapter 14: Diffusive energy balance models in climatology
• Chapter 15: Uniqueness and Stability in the Cauchy Problem for Maxwell and Elasticity Systems
• Chapter 16: On the Unstable Spectrum of the Euler Equation
• Chapter 17: Decomposition en Profils Des Solutions de L’equation Des Ondes Semi Lineaire Critique a L’exterieur D’un Obstacle Strictement Convexe
• Chapter 18: Upwind Discretizations of a Steady Grade-Two Fluid Model in Two Dimensions
• Chapter 19: Stability of Thin Layer Approximation of Electromagnetic Waves Scattering by Linear and Non Linear Coatings
• Chapter 20: Remarques Sur La Limite α → 0 Pour Les Fluides de Grade 2
• Chapter 21: Remarks on the Kompaneets Equation, a Simplified Model of the Fokker-Planck Equation
• Chapter 22: Singular Perturbations Without Limit in the Energy Space. Convergence and Computation of the Associated Layers
• Chapter 23: Optimal Design of Gradient Fields with Applications to Electrostatics
• Chapter 24: A Blackbox Reduced-Basis Output Bound Method for Noncoercive Linear Problems
• Chapter 25: Simulation of Flow in a Glass Tank
• Chapter 26: Control Localized on thin Structures for Semilinear Parabolic Equations
• Chapter 27: Stabilite Des Ondes de Choc de Viscosite Qui Peuvent Etre Caracteristiques