Readership: Graduates and researchers in mathematics, the physical sciences and engineering
Juan Luis Vázquez, Universidad Autónoma de Madrid
"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 generality and depth, is also notable for its author's concern, throughout, to keep the important issues about varieties clearly in the foreground ... [the book] succeeds admirably, in the reviewer's opinion, in introducing its difficult subject at a level appropriate for preparing future workers in the field." - Vicentiu Radulescu, Mathematical Reviews Issue 2007k
Preface Part I 1: Preliminaries 2: Smoothing effect and time decay. Data in L¹(Rn) or M(Rn) 3: Smoothing effect and time decay from Lp or Mp 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 8: 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
