Nonlinear Partial Differential Equations and Their Applications

Nonlinear Partial Differential Equations and Their Applications, 1st Edition

Collège de France Seminar Volume XIV

Nonlinear Partial Differential Equations and Their Applications, 1st Edition,D. Cioranescu,J.-L. Lions†,ISBN9780444511034


North Holland



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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.



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

D. Cioranescu

Affiliations and Expertise

Université Paris VI, France

Information about this author is currently not available.

Nonlinear Partial Differential Equations and Their Applications, 1st Edition

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
(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
(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
(D. Serre).

Quotes and 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)

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