Analytic Inequalities and Their Applications in PDEs

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Birkhäuser, Feb 13, 2017 - Mathematics - 564 pages
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.
 

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Contents

Chapter 1 Integral Inequalities
1
Chapter 2 Differential and Difference Inequalities
79
Chapter 3 Attractors for Evolutionary Differential Equations
209
Chapter 4 Global Existence and Uniqueness for Evolutionary PDEs
231
Chapter 5 Global Existence and Uniqueness for Abstract Evolutionary Differential Equations
245
Chapter 6 Global Existence and Asymptotic Behavior for Equations of Fluid Dynamics
257
Chapter 7 Asymptotic Behavior of Solutions for Parabolic and Elliptic Equations
291
Chapter 8 Asymptotic Behavior of Solutions to Hyperbolic Equations
307
Chapter 9 Asymptotic Behavior of Solutions to Thermoviscoelastic Thermoviscoelastoplastic and Thermomagnetoelastic Equations
357
Chapter 10 Blowup of Solutions to Nonlinear Hyperbolic Equations and HyperbolicElliptic Inequalities
393
Chapter 11 Blowup of Solutions to Abstract Equations and Thermoelastic Equations
429
Basic Inequalities
466
Bibliography
497
Index
561
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About the author (2017)

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.