Analytic Inequalities and Their Applications in PDEs

1. Front Matter

   Pages i-xiii

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2. Integral Inequalities

   • Yuming Qin

   Pages 1-78

3. Differential and Difference Inequalities

   • Yuming Qin

   Pages 79-207

4. Attractors for Evolutionary Differential Equations

   • Yuming Qin

   Pages 209-229

5. Global Existence and Uniqueness for Evolutionary PDEs

   • Yuming Qin

   Pages 231-243

6. Global Existence and Uniqueness for Abstract Evolutionary Differential Equations

   • Yuming Qin

   Pages 245-255

7. Global Existence and Asymptotic Behavior for Equations of Fluid Dynamics

   • Yuming Qin

   Pages 257-290

8. Asymptotic Behavior of Solutions for Parabolic and Elliptic Equations

   • Yuming Qin

   Pages 291-306

9. Asymptotic Behavior of Solutions to Hyperbolic Equations

   • Yuming Qin

   Pages 307-356

10. Asymptotic Behavior of Solutions to Thermoviscoelastic, Thermoviscoelastoplastic and Thermomagnetoelastic Equations

    • Yuming Qin

    Pages 357-392

11. Blow-up of Solutions to Nonlinear Hyperbolic Equations and Hyperbolic-Elliptic Inequalities

    • Yuming Qin

    Pages 393-427

12. Blow-up of Solutions to Abstract Equations and Thermoelastic Equations

    • Yuming Qin

    Pages 429-465

13. Appendix: Basic Inequalities

    • Yuming Qin

    Pages 467-496

14. Back Matter

    Pages 497-564

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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
• partial differential equations

“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)

• Department of Applied Mathematics Institute for Nonlinear Science, Donghua University, Shanghai, China

  Yuming Qin

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.

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