Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Equations of Porous Medium Type
Erscheinungsjahr 2006
ISBN: 978-0-19-920297-3
Verlag: OUP Oxford

Buch, Englisch, 250 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 543 g

This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.

Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porous medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.

Autoren/Hrsg.

Vazquez, Juan Luis

Vázquez, Juan Luis

Fachgebiete

• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Technik: Allgemeines
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Naturwissenschaften Physik Physik Allgemein
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

- Preface

- Part I

- 1: Preliminaries

- 2: Smoothing effect and time decay. Data in L¹(R^n) or M(R^n)

- 3: Smoothing effect and time decay from L^p or M^p

- 4: Lower bounds, contractivity, error estimates and continuity

- Part II

- 5: Subcritical range of the FDE. Critical line. Extinction. Backward effect

- 6: Improved analysis of the critical line. Delayed regularity

- 7: Extinction rates and asymptotics for 0