© 2017

Analytic Inequalities and Their Applications in PDEs


Part of the Operator Theory: Advances and Applications book series (OT, volume 241)

Also part of the Advances in Partial Differential Equations book sub series (APDE, volume 241)

About this book


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.


analytic inequalities differential and difference inequalities hyperbolic equations integral inequalities parabolic equations

Authors and affiliations

  1. 1.Department of Applied Mathematics Institute for Nonlinear ScienceDonghua UniversityShanghaiChina

About the authors

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.

Bibliographic information

Industry Sectors
Energy, Utilities & Environment
Finance, Business & Banking


“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)