Analytic Inequalities and Their Applications in PDEs [Paperback]

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.This book presents analytic inequalities and their applications in partial differential equations. Examines integral, differential and difference inequalities, decay rates and blow-up of solutions to various classes of evolutionary differential equations.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.  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 Rdulescu, zbMATH 1362.35002, 2017)

Yuming Qin, born in 1963, is a professor in the Department of Applied Mathematics and the lƒ)