Buch, Englisch, 648 Seiten, Format (B × H): 160 mm x 240 mm, Gewicht: 1073 g
Mathematical Theory
Buch, Englisch, 648 Seiten, Format (B × H): 160 mm x 240 mm, Gewicht: 1073 g
ISBN: 978-0-19-856903-9
Verlag: Oxford University Press
The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications have been proposed in mathematical biology, lubrication, boundary layer theory, and other fields. Each chapter contains a detailed introduction and is supplied with a section of notes, providing comments, historical notes or recommended reading, and exercises for the reader.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematik Allgemein
- Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Technische Thermodynamik
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Physik Allgemein
- Naturwissenschaften Physik Thermodynamik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
Weitere Infos & Material
- Preface
- 1: Introduction
- Part 1
- 2: Main applications
- 3: Preliminaries and basic estimates
- 4: Basic examples
- 5: The Dirichlet problem I. Weak solutions
- 6: The Dirichlet problem II. Limit solutions, very weak solutions and some other variants
- 7: Continuity of local solutions
- 8: The Dirichlet problem III. Strong solutions
- 9: The Cauchy problem. L' theory
- 10: The PME as an abstract evolution equation. Semigroup approach
- 11: The Neumann problem and problems on manifolds
- Part 2
- 12: The Cauchy problem with growing initial data
- 13: Optimal existence theory for nonnegative solutions
- 14: Propagation properties
- 15: One-dimensional theory. Regularity and interfaces
- 16: Full analysis of selfsimilarity
- 17: Techniques of symmetrization and concentration
- 18: Asymptotic behaviour I. The Cauchy problem
- 19: Regularity and finer asymptotics in several dimensions
- 20: Asymptotic behaviour II. Dirichlet and Neumann problems
- Complements
- 21: Further applications
- 22: Basic facts and appendices
- Bibliography
- Index
