Analytic Inequalities and Their Applications in PDEs

by Yuming Qin

Overview

This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.

Product Details

ISBN-13:	9783319008301
Publisher:	Springer International Publishing
Publication date:	02/16/2017
Series:	Operator Theory: Advances and Applications , #241
Edition description:	1st ed. 2017
Pages:	564
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Yuming Qin, born in 1963, is a professor in the Department of Applied Mathematics and the Institute for Nonlinear Science of Donghua University. His research interests are nonlinear evolutionary partial differential equations and their infinite dimensional dynamical systems. He finished more than 20 grants and is currently carrying out three grants from the National Natural Science Foundation of China and from the Shanghai Education Commission. Prof. Qin is presently on the editorial boards of four international journals and has published over 80 mathematical articles, among them more than 50 SCI articles, as well as four Birkhäuser monographs since 2008.

Table of Contents

Preface.- 1 Integral Inequalities.- 2 Differential and Difference Inequalities.- 3 Global Attractors for Evolutionary Differential Equations.- 4 Global Existence and Uniqueness for Evolutionary PDEs.- 5 Asymptotic Behavior for Evolutionary PDEs.-6 Blow-up of Solutions to Evolutionary PDEs.- 7 Appendix: Basic Inequalities.​

Editorial Reviews

The book is well written. It will be a pleasant and very useful tool for advanced students and researchers in mathematics and applied sciences.” (Denise Huet, Mathematical Reviews, November, 2017)

“This book presents in a systematic way several useful analytic inequalities and their applications in partial differential equations. … The book under review is carefully written and suitable for advanced graduate students and researchers … . The preparation offered by the book is sufficient for undertaking research in these areas. The book can also serve as a reference work for professional mathematicians.” (Teodora-Liliana Rădulescu, zbMATH 1362.35002, 2017)

From the Publisher