Bénilan, P. (Philippe) 1940
Overview
Works:  51 works in 149 publications in 3 languages and 1,060 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Collector, Editor, Honoree, Thesis advisor, Other, Publishing director, Dedicatee 
Classifications:  QA3, 510.8 S 
Publication Timeline
.
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
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
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: HamiltonJacobi equations, the porous medium equation, reaction diffusion systems, integrodifferential equations and viscoelasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein Uhlenbeck operator. Also in this special volume, the legendary work of BenilanBrezis on ThomasFermi Theory is published for the first time
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: HamiltonJacobi equations, the porous medium equation, reaction diffusion systems, integrodifferential equations and viscoelasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein Uhlenbeck operator. Also in this special volume, the legendary work of BenilanBrezis on ThomasFermi Theory is published for the first time
Séminaire les semigroupes et les equations d'evolution : années 197273, 197374 by
P Bénilan(
Book
)
13 editions published between 1972 and 1979 in French and held by 39 WorldCat member libraries worldwide
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
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 uptodate 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 highspeed 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 NavierStokes 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
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 uptodate 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 highspeed 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 NavierStokes 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
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
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)
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
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
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 wellknown that solving the initialvalue 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 initialvalue problems with rough initial data
5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
It is wellknown that solving the initialvalue 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 initialvalue 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
4 editions published in 1987 in French and Undetermined and held by 6 WorldCat member libraries worldwide
Opérateurs maximaux monotones et semigroupes 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
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
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
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
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
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
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
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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Related Identities
 Robert, Jacques 1929 Other Author Editor
 Brézis, H. (Haim) Author Editor
 Dautray, Robert Author
 Arendt, Wolfgang 1950 Editor
 Pierre, Michel 1949 Editor
 Lions, JacquesLouis 19282001
 Authier, Marc Collector Author
 Artola, Michel (1932....). Collector
 Lions, JacquesLouis (19282001)
 Journées d'analyse non linéaire
Associated Subjects
Calculus, Operational Differential equations Differential equations, Elliptic Differential equations, Linear Differential equations, Nonlinear Differential equations, Parabolic Differential equations, Partial Engineering mathematics Equations Evolution equations Evolution equations, Nonlinear Hilbert space Initial value problems Mathematical analysis Mathematical physics Mathematics Mechanics Monotone operators Nonlinear operators Nonlinear theories Numerical analysis ScienceMathematics Semigroups TechnologyMathematics