Nonlinear partial differential equations and their applications : Collège de France seminar

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Bibliographic Information

Nonlinear partial differential equations and their applications : Collège de France seminar

H. Brézis & J.L. Lions, editors ; D. Cioranescu, coordinator

（Research notes in mathematics, 53, 60, 70, 84, 93, 109, 122）（Pitman research notes in mathematics series, 166,181, 220, 299, 302, 391）

Pitman Advanced Pub. Program, 1982-

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Note

Lectures presented at the weekly Seminar on Applied Mathematics, Collège de France, Paris

English and French

Includes bibliographical references

Description and Table of Contents

Volume

v. 11 ISBN 9780582238008

Description

Contains papers presented by leading international experts at the well-established weekly seminar held at the College de France.

Table of Contents

Includes papers by: M Ben-Artzi C Bernardi, Y Maday & A T Patera Y Brenier J M Coron B Dacorogna M G Garroni, V A Solonnikov & M A Vivaldi S Jaffard D Kinderlehrer & P Pedregal H Le Dret J M Morel G Raugel & G R Sell D Serre L Tartar M Vanninathan
Volume

v. 12 ISBN 9780582238015

Description

This book contains the texts of selected lectures delivered at weekly seminars at the College de France during the period 1991-93. The main theme of the papers is recent work in the field of partial differential equations - a field of growing importance both in pure and applied mathematics.

Table of Contents

  • To scale convergence - a new method in periodic homogenizations, G. Allaire
  • some remarks concerning the theory of exact controllability and stabilization for the wave equation, C. Bardos
  • equi-coercivity of variational problems - the role of recession functions, G. Bouchitte and P. Suquet
  • boundary value problems for forced superlinear secon order ordinary differential equations, A. Capietto, J. Mawhin and F. Zanolin
  • existence des nappes de tourbillon designe fixe en dimension deux, J.M. Delort
  • microlocal analysis of compactness, P. Gerard
  • majorations en norme du maximum del la resolvante du laplacien dans une polygone, P. Grisvard
  • homogeneisation non locale d'equations hyperboliques, K. Hamdache
  • quelques proprietes des series lacunaires utiles dans l'etude des vibrations elastiques, A. Haraux
  • variational problems in homogenization theory, S.M. Kozlov
  • perfect flow past a nonlinearly ealstic panel, M. Lanza de Cristoforis and S. Antman
  • turbulence et structures - coherentes dans les fluides, M. Lesieur
  • paraxial approximation of the stationary Vlasov-Maxwell equations, P.A. Raviart
  • singularities and junctions in elasticity, E. Sanchez-Panencia
  • oscillations non-lineaires de haute frequence, dim=1, D. Serre
  • functionals with surface terms on a free singular set, S. Solimini
  • estimates for the heat kernel of second order elliptic equations, D. Stroock.
Volume

v. 13 ISBN 9780582369269

Description

This book presents the texts of selected lectures on recent work in the field of nonlinear partial differential equations delivered by leading international experts at the well-established weekly seminar held at the College de France. Emphasis is on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis, and engineering. Proceedings of this seminar will be of particular interest to postgraduate students and specialists in the area of nonlinear partial differential equations.

Table of Contents

A Nonlinear Lax-Milgram Lemma Arising in the Modeling of Elastomers. Regularity for Solutions to the Equation of Surfaces of Prescribed Mean Curvature Using the Coarea Formula. H-Convergence for Perforated Domains. Some Mathematical Problems in Marine Modelling. A Modelling of the Stability of Aluminium Electrolysis Cells. Dense Oscillations for the Compressible 2-d Euler Equations. The Hysteretic Event in the Computation of Magnetism and Magnetostriction. From Three-Dimensional Elasticity to the Nonlinear Membrane Model. Turbulence et structures coherentes dans les fluides. Construction d'une base speciale pour la resolution de quelques problemes non lineaires d'Oceanographie physique en dimension deux. Homogenization of Lattice-Like Domains: L-Convergence. Time Decays: An Analogy between Kinetic Transport, Schroedinger and Gas Dynamics Equations. Theoreme d'unicite et controle pour les equations hyperboliques. Shock Waves in General Relativity - A Generalization of the Oppenheimer-Snyder Model for Gravitational Collapse. Nonlinear Wave Equations. Mathematical Models of Hysteresis - A Survey.

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