Nonlinear partial differential equations with applications
By: Tomáš Roubíček.
Series: International series of numerical mathematics ;; v. 153
Publisher: Birkhauser Verlag
Published: 2005
Place of publication: Boston, MA
Language: eng
Number of pages: 405
ISBN-13: 9783764372931
Subjects: Differential equations, Partial; Differential equations, Nonlinear; Continuum mechanics; Thermodynamics
Description: This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. It balances the abstract functional-analysis approach based on nonlinear monotone, pseudomonotone, weakly continuous, or accretive mappings with concrete partial differential equations in their weak (or more general) formulation. Methods of Galerkin or of Rothe are exposed in a large generality. Other methods include various direct methods, regularization, or fixed points. The exposition leads general theory as fast as possible towards the analysis of concrete 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 rather an introduction into the subject while some others form an advanced textbook. The intended audience is graduate and PhD students and researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.
Notes: Includes bibliographical references and index.