Nonlinear Partial Differential Equations with Applications

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Springer Science & Business Media, Jan 17, 2006 - Mathematics - 405 pages
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This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

 

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Contents

Preliminary general material
1
Pseudomonotone or weakly continuous mappings 29
28
Accretive mappings
89
smooth case
109
Nonsmooth problems variational inequalities
125
Implicit variational problems and quasivariational inequalities
156
particular examples
161
Special auxiliary tools
187
On elliptic partial differential equations Ann Scuola
265
Evolution governed by accretive mappings
275
Evolution governed by certain setvalued mappings 305
304
Doublynonlinear problems
321
99
346
particular examples
357
References
383
Index
399

Evolution by pseudomonotone or weakly continuous mappings 199
198
252 Moser J A new proof of De Giorgis theorem concerning the regularity problem
252

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