- Title Pages
- Preface
- Introduction
- Part I Estimates for the PME/FDE
- 1 Preliminaries
- 2 Smoothing effect and time decay. Data in <i>L</i> <sup>1</sup> (R<sup><i>n</i></sup>) or <i>M</i> (R<sup><i>n</i></sup>)
- 3 Smoothing effect and time decay from <i>L</i> <sup><i>p</i></sup> or <i>M</i> <sup><i>p</i></sup>
- 4 Lower bounds, contractivity, error estimates, and continuity
- Part II Study of the subcritical FDE
- 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 < <i>m</i> < <i>m</i> <sub><i>c</i></sub>
- 8 Logarithmic diffusion in 2D and intermediate 1D range
- 9 Superfast FDE
- 10 Summary of main results for the PME/FDE
- Part III Extensions and appendices
- 11 Evolution equations of the <i>p</i>-Laplacian type
- Appendix I. Some analysis topics
- Appendix II. Particles and speeds
- Appendix III. Some Riemannian geometry
- Appendix IV. Some extensions and parallel topics
- Bibliography
- Index
Introduction
Introduction
- Chapter:
- (p.1) Introduction
- Source:
- Smoothing and Decay Estimates for Nonlinear Diffusion Equations
- Author(s):
Juan Luis Vázquez
- Publisher:
- Oxford University Press
This introductory chapter opens with an explanation of the purpose of the book, which is to obtain basic estimates for some particular nonlinear parabolic equations and to derive consequences about qualitative and quantitative aspects of the theory. The technical tools used, goals, contents and distribution, and how to read and use the book are discussed.
Keywords: nonlinear parabolic equations, smoothing, nonlinear diffusion, asymptotic behaviour
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- Title Pages
- Preface
- Introduction
- Part I Estimates for the PME/FDE
- 1 Preliminaries
- 2 Smoothing effect and time decay. Data in <i>L</i> <sup>1</sup> (R<sup><i>n</i></sup>) or <i>M</i> (R<sup><i>n</i></sup>)
- 3 Smoothing effect and time decay from <i>L</i> <sup><i>p</i></sup> or <i>M</i> <sup><i>p</i></sup>
- 4 Lower bounds, contractivity, error estimates, and continuity
- Part II Study of the subcritical FDE
- 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 < <i>m</i> < <i>m</i> <sub><i>c</i></sub>
- 8 Logarithmic diffusion in 2D and intermediate 1D range
- 9 Superfast FDE
- 10 Summary of main results for the PME/FDE
- Part III Extensions and appendices
- 11 Evolution equations of the <i>p</i>-Laplacian type
- Appendix I. Some analysis topics
- Appendix II. Particles and speeds
- Appendix III. Some Riemannian geometry
- Appendix IV. Some extensions and parallel topics
- Bibliography
- Index
