Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population Genetics (Springer Monographs in Mathematics)

From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations Front Matter....Pages i-xviii Overview of Mathematical Methods in Partial Differential Equations....Pages 1-18 Liouville Type Theorems for Elliptic Operators in Divergence Form....Pages 19-27 Blow-Up Boundary Solutions of the Logistic Equation....Pages 29-115 Singular Lane–Emden–Fowler Equations and Systems....Pages 117-165 Singular Elliptic Inequalities in Exterior Domains....Pages 167-210 Two Quasilinear Elliptic Problems....Pages 211-243 Some Classes of Polyharmonic Problems....Pages 245-266 Large Time Behavior of Solutions for Degenerate Parabolic Equations....Pages 267-286 Reaction-Diffusion Systems Arising in Chemistry....Pages 287-335 Pattern Formation and the Gierer–Meinhardt Model in Molecular Biology....Pages 337-367 Back Matter....Pages 369-391 This book shows how to apply theoretical mathematical models to unravel the mechanisms involved in processes found in mathematical physics and the biosciences. It is a unique collection of abstract methods that deploy nonlinear partial differential equations.