Analytic Inequalities and Their Applications in PDEs
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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Chapter 2 Differential and Difference Inequalities
Chapter 3 Attractors for Evolutionary Differential Equations
Chapter 4 Global Existence and Uniqueness for Evolutionary PDEs
Chapter 5 Global Existence and Uniqueness for Abstract Evolutionary Differential Equations
Chapter 6 Global Existence and Asymptotic Behavior for Equations of Fluid Dynamics
Chapter 7 Asymptotic Behavior of Solutions for Parabolic and Elliptic Equations
Chapter 8 Asymptotic Behavior of Solutions to Hyperbolic Equations
Chapter 9 Asymptotic Behavior of Solutions to Thermoviscoelastic Thermoviscoelastoplastic and Thermomagnetoelastic Equations
Chapter 10 Blowup of Solutions to Nonlinear Hyperbolic Equations and HyperbolicElliptic Inequalities
Chapter 11 Blowup of Solutions to Abstract Equations and Thermoelastic Equations
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