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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.
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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)
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)
From the reviews of the second edition:
"The monograph is concerned with the study of various classes of nonlinear elliptic and parabolic partial differential equations with many applications. ... The book is very well written, the presentation is clear and rigorous, and it contains a comprehensive bibliography. This monograph will be useful to all persons who are interested in nonlinear partial differential equations or systems and their applications." (Rodica Luca Tudorache, zbMATH, Vol. 1270, 2013)
"The monograph is concerned with the study of various classes of nonlinear elliptic and parabolic partial differential equations with many applications. ... The book is very well written, the presentation is clear and rigorous, and it contains a comprehensive bibliography. This monograph will be useful to all persons who are interested in nonlinear partial differential equations or systems and their applications." (Rodica Luca Tudorache, zbMATH, Vol. 1270, 2013)