Nonlinear Partial Differential Equations and Their Applications book cover

Nonlinear Partial Differential Equations and Their Applications

Collège de France Seminar Volume XIV

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.

18.07

Audience
Libraries in Mathematical Departments, Institutes of Research in Pure and Applied Mathematics

Hardbound, 664 Pages

Published: June 2002

Imprint: North-holland

ISBN: 978-0-444-51103-4

Reviews

  • "...it is shown that the Kompaneets equation has solutions which blow up in finite time." Oleg Titow, (Berlin), in: (Zentralblatt für Mathematik, Vol. 1034, 2004)

Contents

  • An introduction to critical points for integral functionals (D. Arcoya, L. Boccardo).
    A semigroup formulation for electromagnetic waves in dispersive dielectric media (H.T. Banks, M.W. Buksas).
    Limite non visqueuse pour les fluides incompressibles axisymétriques (J. Ben Ameur, R. Danchin).
    Global properties of some nonlinear parabolic equations (M. Ben-Artzi).
    A model for two coupled turbulent flows. Part I: analysis of the system (C. Bernardi, T. Chacón Rebollo, R. Lewandowski, F. Murat).
    Détermination de conditions aux limites en mer ouverte par une méthode de contrôle optimal (F. Bosseur, P. Orenga).
    Effective diffusion in vanishing viscosity (F. Campillo, A. Piatnitski).
    Vibration of a thin plate with a "rough" surface (G. Chechkin, D. Cioranescu).
    Anisotropy and dispersion in rotating fluids (J.-Y. Chemin, B. Desjardins, I. Gallagher, E. Grenier).
    Integral equations and saddle point formulation for scattering problems (F. Collino, B. Despres).
    Existence and uniqueness of a strong solution for nonhomogeneous micropolar fluids (C. Conca, R. Gormaz, E. Ortega, M. Rojas).
    Homogenization of Dirichlet minimum problems with conductor type periodically distributed constraints (R. De Arcangelis).
    Transport of trapped particles in a surface potential (P. Degond).
    Diffusive energy balance models in climatology (J.I. Díaz).
    Uniqueness and stability in the Cauchy problem for Maxwell and elasticity systems (M. Eller, V. Isakov, G. Nakamura, D. Tataru).
    On the unstable spectrum of the Euler equation (S. Friedlander).
    Décomposition en profils des solutions de l'équation des ondes semi linéaire critique à l'extérieur d'un obstacle strictement convexe (I. Gallagher, P. Gérard).
    Upwind discretizations of a steady grade-two fluid model in two dimensions (V. Girault, L.R. Scott).
    Stability of thin layer approximation of electromagnetic waves scattering by linear and non linear coatings (H. Haddar, P. Joly).
    Remarques sur la limite → 0 pour les fluides de grade 2 (D. Iftimie).
    Remarks on the Kompaneets equation, a simplified model of the Fokker-Planck equation (O. Kavian).
    Singular perturbations without limit in the energy space. Convergence and computation of the associated layers (D. Leguillon, E. Sanchez-Palencia, C. de Souza).
    Optimal design of gradient fields with applications to electrostatics (R. Lipton, A.P. Velo).
    A blackbox reduced-basis output bound method for noncoercive linear problems (Y. Maday, A.T. Patera, D.V. Rovas).
    Simulation of flow in a glass tank (V. Nefedov, R.M.M. Mattheij).
    Control localized on thin structures for semilinear parabolic equations (P.A. Nguyen, J.-P. Raymond).
    Stabilité des ondes de choc de viscosité qui peuvent être caractéristiques (D. Serre).

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