Nonlinear PDEs Mathematical Models in Biology, Chemistry and Population Genetics /

• Κύριοι συγγραφείς: Ghergu, Marius (Συγγραφέας), Rӑdulescu, Vicenţiu D. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Mathematical physics.; Calculus of variations.; Partial Differential Equations.; Calculus of Variations and Optimal Control; Optimization.; Mathematical Applications in the Physical Sciences.; Global Analysis and Analysis on Manifolds.; Dynamical Systems and Ergodic Theory.

 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. 

 Viorel Barbu: Foreword -- 1.Overview of merhods in PDEs -- 2.Liouville Type Theorems for Elliptic Operators in Divergence Form -- 3.Blow-up Boundary Solutions -- 4.Singular Lane-Emden-Fowler Equations and Systems.- 5.Singular Elliptic Inequalities in Exterior Domains -- 6.Two Quasilinear Elliptic Problems -- 7.Some Classes of Polyharmonic Problems -- 8.Large Time Behavior of Solutions for Degenerate Parabolic Equations -- 9.Rection-Diffusion Systems in Chemistry -- 10.Pattern Formation and Gierer-Meinhardt Model -- Appendices -- References -- Index.    .