Nonlinear partial differential equations with applications / Tomáš Roubíček

Auteur: Roubíček, Tomáš (1956-) - AuteurType de document: Livre numériqueCollection: International series of numerical mathematics ; 153Langue: anglaisÉditeur: Basel : Birkhäuser, 2013 ISBN: 9783034805124 Note: Publisher's description: "This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook. "The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and Ph.D. students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.'' Sujets MSC: 35J60 Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations
35K55 Partial differential equations -- Parabolic equations and systems -- Nonlinear parabolic equations
35J87 Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
35K86 Partial differential equations -- Parabolic equations and systems -- Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
47H04 Operator theory -- Nonlinear operators and their properties -- Set-valued operators
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Publisher's description: "This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook.
"The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and Ph.D. students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.''

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