Monotone Operators in Banach Space and Nonlinear Partial Differential Equations (Mathematical Surveys and Monographs) - Brossura

Showalter, R. E.

Brossura

ISBN 10: 0821893971 ISBN 13: 9780821893975

Casa editrice: American Mathematical Society, 2014

Riassunto

The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed. The origins of a representative sample of such problems are given in the appendix.

Dettagli dell?edizione

• Editore: American Mathematical Society
• Data di pubblicazione: 2014
• ISBN 10: 0821893971
• ISBN 13: 9780821893975
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 278