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Smoothing and decay estimates for nonlinear diffusion equations : equations of porous medium type

Author: J L Vazquez
Publisher: Oxford : Oxford University Press, 2006.
Series: Oxford lecture series in mathematics and its applications, 33.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations which can be seen as nonlinear variations of the classical heat equation. They appear in different branches of Physics, Chemistry, Biology, and Engineering, and are also quite relevant in differential geometry. Much of the modern theory of such equations is based on estimates and functional analysis."--Jacket.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J L Vazquez
ISBN: 0199202974 9780199202973
OCLC Number: 68770240
Description: xiii, 234 pages : illustrations ; 24 cm.
Contents: 1. Preliminaries --
2. Smoothing effect and time decay : data in L[superscript 1](R[superscript n]) or M(R[superscript n]) --
3. Smoothing effect and time decay from L[superscript p] or M[superscript p] --
4. Lower bounds, correctivity, error estimates, and continuity --
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 <m <m[subscript c] --
8. Logarithmic diffusion in 2D and intermediate 1D range --
9. Superfast FDE --
10. Summary of main results for the PME/FDE --
11. Evolution equations of the p-Laplacian type.
Series Title: Oxford lecture series in mathematics and its applications, 33.
Responsibility: Juan Luis Vázquez.
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Abstract:

This text is concerned with quantitative aspects of the theory of nonlinear diffusion equations, which appear as mathematical models in different branches of Physics, Chemistry, Biology and  Read more...

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This book is intended to introduce graduate students to the methods and results of nonlinear diffusion equations of porous medium type, as practised today. The present text, remarkable for Read more...

 
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