Juan Luis Vázquez

Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Equations of Porous Medium Type

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Hurst & Co.
• Seitenzahl: 250
• Erscheinungstermin: 12. Oktober 2006
• Englisch
• Abmessung: 234mm x 157mm x 18mm
• Gewicht: 499g
• ISBN-13: 9780199202973
• ISBN-10: 0199202974
• Artikelnr.: 21675721

Inhaltsangabe

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 08: Logarithmic diffusion in 2-d and intermediate 1-d range
9: Super-fast FDE
10: Summary of main results for the PME/FDE
Part III
11: Evolution equations of the p-Laplacian type
12: Appendices
Bibliography
Index