Nonlinear Partial Differential Equations with Applications (No TOC)

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 PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems. ------ __The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (...) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world.__ (Mathematical Reviews) 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 Front Matter....Pages i-xx Preliminary general material....Pages 1-27 Front Matter....Pages 29-29 Pseudomonotone or weakly continuous mappings....Pages 31-93 Accretive mappings....Pages 95-114 Potential problems: smooth case....Pages 115-131 Nonsmooth problems; variational inequalities....Pages 133-170 Systems of equations: particular examples....Pages 171-198 Front Matter....Pages 199-199 Special auxiliary tools....Pages 201-211 Evolution by pseudomonotone or weakly continuous mappings....Pages 213-301 Evolution governed by accretive mappings....Pages 303-333 Evolution governed by certain set-valued mappings....Pages 335-349 Doubly-nonlinear problems....Pages 351-391 Systems of equations: particular examples....Pages 393-448 Back Matter....Pages 449-476

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. 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.

Preface Preface to the 2nd edition Notational conventions 1 Preliminary general material I Steady-state problems 2 Pseudomonotone or weakly continuous mappings 3 Accretive mappings 4 Potential problems: smooth case 5 Nonsmooth problems; variational inequalities 6. Systems of equations: particular examples II Evolution problems 7 Special auxiliary tools 8 Evolution by pseudomonotone or weakly continuous mappings 9 Evolution governed by accretive mappings 10 Evolution governed by certain set-valued mappings 11 Doubly-nonlinear problems 12 Systems of equations: particular examples References Index. 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. Concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. This title includes exposition that leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, and modeling of biological systems. This book examines quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The 2nd edition simplifies and extends the exposition and augments applications in thermally coupled systems, magnetism, and more.