Bénilan, P. (Philippe) 1940-

Overview
Works: 51 works in 149 publications in 3 languages and 1,060 library holdings Conference papers and proceedings Author, Collector, Editor, Honoree, Thesis advisor, Other, Publishing director, Dedicatee QA3, 510.8 S
Publication Timeline
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Most widely held works by P Bénilan
Proceedings, Beasançon, France, June 1977 by Journées d'analyse non linéaire( Book )

23 editions published between 1978 and 2008 in 4 languages and held by 409 WorldCat member libraries worldwide

Recent advances in nonlinear elliptic and parabolic problems : proceedings of an international conference, Nancy, France, March 1988 by International conference on recent advances in nonlinear elliptic and parabolic problems( Book )

15 editions published in 1989 in English and held by 200 WorldCat member libraries worldwide

Nonlinear evolution equations and related topics : dedicated to Philippe Bénilan by Wolfgang Arendt( Book )

4 editions published in 2004 in English and held by 67 WorldCat member libraries worldwide

Philippe Benilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. This present volume is dedicated to him and contains research papers written by highly distinguished mathematicians. They are all related to Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations. Special topics include: Hamilton-Jacobi equations, the porous medium equation, reaction diffusion systems, integro-differential equations and visco-elasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein Uhlenbeck operator. Also in this special volume, the legendary work of Benilan-Brezis on Thomas-Fermi Theory is published for the first time
Séminaire les semi-groupes et les equations d'evolution : années 1972-73, 1973-74 by P Bénilan( Book )

13 editions published between 1972 and 1979 in French and held by 39 WorldCat member libraries worldwide

Spectre des opérateurs by Robert Dautray( Book )

4 editions published between 1984 and 1988 in French and held by 39 WorldCat member libraries worldwide

Mathematical analysis and numerical methods for science and technology by Robert Dautray( Book )

13 editions published between 1990 and 2000 in English and held by 30 WorldCat member libraries worldwide

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences. The main physical examples examined in the 6 volumes are presented in Chapter I: Classical Fluids and the Navier-Stokes System; Linear Elasticity, Linear Viscoelasticity, Electromagnetism and Maxwell's Equation, Neutronics, and Quantum Physics. Then a first examination of the mathematical models is given. Chapter II is devoted to the study of the Laplacian operator by methods which only use classical tools
Journées d'Analyse Non Linéaire Proceedings, Besançon, France, June 1977 by P Bénilan( )

1 edition published in 1978 in French and held by 28 WorldCat member libraries worldwide

Physical origins and classical methods by Robert Dautray( Book )

2 editions published in 1990 in English and held by 18 WorldCat member libraries worldwide

Équations d'évolution dans un espace de Banach quelconque et applications by P Bénilan( Book )

5 editions published in 1972 in French and Undetermined and held by 13 WorldCat member libraries worldwide

ETANT DONNES UN OPERATEUR (NON LINEAIRE) ACCRETIF A D'UN ESPACE DE BANACH QUELCONQUE X, F APPARTIENT A L**(1)(O,T; X) ET N::(0) APPARTIENT A D(A), D(A), ON ETUDIE L'EQUATION D'EVOLUTION DU/DT+AU APPARTIENT A F, U(0)=U::(0). LE TRAVAIL EST DIVISE EN TROIS CHAPITRES: AU CHAPITRE 0 ON INTRODUIT LES INSTRUMENTS DONT ON SE SERT (LE PRODUIT <.,.>::(DELTA ), LES OPERATEURS ACCRETIFS, LA DIVISIBILITE DES FONCTIONS VECTORIELLES); AU CHAPITRE 1 ON ETUDIE LES SOLUTIONS INTEGRALES DANS UN CADRE ABSTRAIT ET ENFIN AU CHAPITRE 2 ON APPLIQUE CES RESULTATS A DEUX EQUATIONS D'EVOLUTION DANS L'ESPACE L**(1)
Recent advances in nonlinear elliptic and parabolic equations( Book )

4 editions published in 1989 in English and held by 12 WorldCat member libraries worldwide

A semilinear elliptic equation in L¹(IR [superscript n]) by P Bénilan( Book )

6 editions published in 1975 in English and held by 7 WorldCat member libraries worldwide

Regularizing effects of homogeneous evolution equations by Michael G Crandall( Book )

5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide

It is well-known that solving the initial-value problem for the heat equation forward in time takes a 'rough' initial temperature into a temperature which is smooth at later times t> greater than 0. One aspect of this is the validity of certain estimates on tut when u is a solution of the heat equation. In this paper we prove related estimates on nonlinear evolution equations which are governed by homogeneous nonlinearities. The results apply to classes of nonlinear diffusion equations and to conservation laws. The results are interesting from the point of view of identifying a new 'regularization' mechanism and the estimates themselves cast new light on the nature of the solutions of some initial-value problems with rough initial data
Transformations, Sobolev, opérateurs by Robert Dautray( Book )

4 editions published in 1987 in French and Undetermined and held by 6 WorldCat member libraries worldwide

Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert by H Brézis( Book )

1 edition published in 1971 in French and held by 6 WorldCat member libraries worldwide

Evolution equations : proceedings in honor of J.A. Goldstein's 60th birthday( Book )

1 edition published in 2003 in English and held by 5 WorldCat member libraries worldwide

Proceedings by Journees d'analyse non lineaire( Book )

1 edition published in 1978 in English and held by 5 WorldCat member libraries worldwide

The continuous dependence on $\varphi$ of solutions of $u_ t-\Delta\varphi (u)=0$ by P Bénilan( Book )

4 editions published in 1979 in English and held by 4 WorldCat member libraries worldwide

Analyse mathématique et calcul numérique pour les sciences et les techniques by Robert Dautray( Book )

3 editions published in 1987 in French and held by 4 WorldCat member libraries worldwide

L'opérateur de laplace by Marc Authier( Book )

3 editions published in 1987 in French and Undetermined and held by 3 WorldCat member libraries worldwide

Concavity of Solutions of the Porous Medium Equation by Mathematics Research Center (United States. Army)( Book )

3 editions published in 1985 in English and held by 3 WorldCat member libraries worldwide

The flow of a gas through a porous medium is governed by a degenerate quasilinear parabolic equation. It is known that the nonnegative solutions to this equation possess a lower bound for the second derivative of the pressure in the spatial variables. This bound plays an important role in the mathematical treatment and is related to the entropy of the flow. Since the solutions exhibit interfaces across which v sub x jumps positively, no upper bound is possible globally for v subxx. Nevertheless it is proven that the concavity of v(., t) in the region where v is positive is preserved in time. This is in itself an interesting geometric property of the solution. It also allows one to obtain precise information about the asymptotic behaviour of the flow

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Alternative Names
Bénilan, P.

Bénilan, Philipp 1940-2001

Bénilan, Philippe 1940-

Languages
English (61)

French (48)

German (1)

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