Nonlinear Partial Differential Equations with Applications

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This book focuses on quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. It guides readers through the general theory based on abstract (pseudo-) monotone or accretive operators, progressing swiftly to the analysis of specific differential equations with applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, biological systems, and mechanical engineering. Some sections serve as an introduction, while others function as an advanced textbook. The second edition enhances the exposition and expands applications, particularly in thermally coupled systems and magnetism. It targets graduate and PhD students, as well as researchers in partial differential equations and mathematical modeling of distributed parameter systems. The monograph offers extensive material on both the abstract theory of steady-state and evolution equations of monotone and accretive types, as well as concrete applications to nonlinear partial differential equations in mathematical modeling. The organization is effective, and the presentation is concise yet clear, elegant, and rigorous. This book is a valuable addition to existing literature and will be beneficial for engineers, physicists, biologists, and other scientists interested in analyzing nonlinear differential models in real-world contexts.