Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population GeneticsThe 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. |
Contents
1 | |
Liouville Type Theorems for Elliptic Operatorsin Divergence Form | 19 |
BlowUp Boundary Solutions of the Logistic Equation | 29 |
Singular LaneEmdenFowler Equations and Systems | 116 |
Singular Elliptic Inequalities in Exterior Domains | 167 |
Two Quasilinear Elliptic Problems | 211 |
Some Classes of Polyharmonic Problems | 245 |
Large Time Behavior of Solutions for Degenerate Parabolic Equations | 267 |
ReactionDiffusion Systems Arising in Chemistry | 287 |
Pattern Formation and the GiererMeinhardt Model in Molecular Biology | 337 |
CaffarelliKohnNirenberg Inequality | 368 |
Estimates for the Green Function Associatedto the Biharmonic Operator | 373 |
377 | |
387 | |
Other editions - View all
Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population ... Marius Ghergu,Vicentiu RADULESCU No preview available - 2011 |
Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population ... Marius Ghergu,Vicentiu RADULESCU No preview available - 2011 |
Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population ... Marius Ghergu,Vicentiu RADULESCU No preview available - 2013 |
Common terms and phrases
arguments Assume that f assumption asymptotically ball boundary blow-up solution classical solution cö(x compact set completes the proof concludes the proof consider continuous function contradiction converges Corollary deduce defined denote derive Dirichlet Dirichlet boundary condition eigenvalue elliptic problems entire large solution estimate exist c1 f satisfies finishes the proof finite follows Furthermore Ghergu global solution Green function Hence Hölder's inequality holds implies inequality Integrating Keller–Osserman condition Kelvin transform Laplace operator Mathematics maximum principle minimal solution mountain pass theorem Neumann boundary condition nG(Q nonconstant solution nondecreasing nonnegative obtain open set positive constant positive solution proof of Theorem prove radially symmetric real numbers Remark resp sequence Sobolev space solution of problem standard elliptic subsolution tion unique solution weak solution x e Q yields