Foreword 
Introduction 
Notation 
 Physical notation 
 Mathematical notation 
Part 1. Wave Equations 
Chapter 1.  PseudoHyperbolic Model Equations 
 1.1 Equations of Internal Waves in Fluids 
 1.2 Equations of IonSound Waves in Plasma 
Chapter 2.  BlowUp of Solutions of PseudoHyperbolic Equations 
 2.1 BlowUp of Internal Gravitational Waves 
 2.2 BlowUp of IonSound Waves in Plasma 
 2.3 BlowUp of IonSound Waves in Plasma with Strong SpatialTime Dispersion 
Chapter 3.  Nonlinear Dynamical Boundary Conditions 
 3.1 BlowUp of Solutions of the Equation of IonSound Waves with Nonlinear Dynamical Boundary Condition 
 3.2 BlowUp of Solutions of the Equation of GravitationalGyroscopic Waves with Nonlinear Boundary Conditions 
Chapter 4.  Model Systems of PseudoHyperbolic Equations 
 4.1 System of Equations of IonSound Waves in Plasma 
 4.2 Hydrodynamic System of Oskolkov Equations 
Part 2. Nonlocal Equations 
Chapter 5.  Model Nonlinear Nonlocal Equations of Sobolev Type 
 5.1 Equations of QuasiStationary Fields in Crystalline Semiconductors 
 5.2 Model Equations 
 5.3 Model Equations for the Function h(t) 
Chapter 6.  BlowUp of Solutions of Nonlocal Sobolev Equations 
 6.1 BlowUp of Solutions of an InitialBoundaryValue Problem for the Nonlinear Nonlocal BenjaminBonaMahonyBurgers Equation with Sources 
 6.2 BlowUp of Solutions of the Nonlinear Nonlocal BenjaminBonaMahonyBurgers Wave Equation with a Nonlocal Source 
 6.3 BlowUp of Solutions of Nonlocal Dissipative RosenauBurgers Equation with a Source 
 6.4 BlowUp of Solutions of the Nonlinear Nonlocal Equation of Spin Waves with a Source 
Chapter 7.  BlowUp of Solutions of Nonlocal Sobolev Systems 
 7.1 BlowUp of Solutions of One System of Nonlocal Equations with Sources 
 7.2 BlowUp of Solutions of the Nonlinear Nonlocal Oskolkov System with a Source 
Chapter 8.  BlowUp of Solutions of the Abstract Cauchy Problem 
 8.1 Preliminary conditions 
 8.2 Auxiliary results 
 8.3 Local Solvability in the Strong Generalized Sense 
 8.4 BlowUp of Strong Generalized Solutions 
Chapter 9.  BlowUp of Solutions of Problems with Nonlinear Boundary Conditions 
 9.1 BlowUp of Solutions of One Problem with Nonlinear Neumann Boundary condition 
 9.2 BlowUp in the Problem with Nonlinear Evolution Nonlocal Boundary Condition 
Part 3. Wave and Nonlocal Equations 
Chapter 10.  Model Nonlinear Nonlocal Wave Equations of Sobolev Type 
 10.1 General Systems of Equations of QuasiStationary Fields 
 10.2 Time Dispersion 
 10.3 Spatial Dispersion 
 10.4 Nonlinear Factors 
 10.5 Model IntegroDifferential Equations and SobolevType Equations 
Chapter 11.  BlowUp of Solutions of Wave IntegroDifferential Equations of Sobolev Type 
 11.1 BlowUp of Solutions of One Equation of Third Order 
 11.2 Blowup of Solutions of One Nonlocal Equation of Fifth Order 
 11.3 Equations of a Tunnel Diode 
Appendix A.  Some Results Of Nonlinear Analysis 
 A.1  Sobolev Spaces W^{s,p}(Omega), W^{s,p}_{0}(Omega), and W^{s,p}(Gamma) 
 A.2  Weak and ast Weak Convergence 
 A.3  Chain Rule for Frechet Derivatives 
 A.4  Caratheodori Functions. Nemytsky Operators. Krasnosel'sky Theorem 
 A.5  Compact Continuous Operators and Completely Continuous Operators 
 A.6  Compactness Lemma of J.L.Lions 
 A.7  BrowderMinty Theorem 
 A.8  On the System of Ordinary Differential Equations in the Galerkin Method 
 A.9  Two Equivalent Definitions of a Weak Solution in the Sense of L^{2}(0, T; B) 
 A.10  Basic IntegroDifferential Inequalities 
 A.11  Auxiliary Lemmas about Homogeneous Functionals 
 A.12  Dense Embeddings of Banach Spaces 
 A.13  Frechet Derivative of the pLaplacian 
Appendix 
Index 
Appendix 
Bibliography
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