Analytic Inequalities and Their Applications in PDEs

1. Integral Inequalities
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2. Differential and Difference Inequalities
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3. Attractors for Evolutionary Differential Equations
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4. Global Existence and Uniqueness for Evolutionary PDEs
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5. Global Existence and Uniqueness for Abstract Evolutionary Differential Equations
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6. Global Existence and Asymptotic Behavior for Equations of Fluid Dynamics
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7. Asymptotic Behavior of Solutions for Parabolic and Elliptic Equations
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8. Asymptotic Behavior of Solutions to Hyperbolic Equations
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9. Asymptotic Behavior of Solutions to Thermoviscoelastic, Thermoviscoelastoplastic and Thermomagnetoelastic Equations
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10. Blow-up of Solutions to Nonlinear Hyperbolic Equations and Hyperbolic-Elliptic Inequalities
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11. Blow-up of Solutions to Abstract Equations and Thermoelastic Equations
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12. Appendix: Basic Inequalities
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Keywords: Mathematics, Partial Differential Equations, Classical Mechanics, Operator Theory, Mathematical Physics