Nonlinear Partial Differential Equations with Applications
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.
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From the reviews:
"The book under review is mainly devoted to the study of both steady-state (Part I) and evolution (Part II) boundary value problems . . The organization of the material is well done, and the presentation . is clear, elegant and rigorous. . In conclusion, primarily addressed to graduate and Ph.D. students and researchers . this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists . ." (Ioan I. Vrabie, Mathematical Reviews, Issue 2007 e)
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