Foreword |

Introduction |

Notation |

| Physical notation |

| Mathematical notation |

Part 1. Wave Equations |

Chapter 1. | Pseudo-Hyperbolic Model Equations |

| 1.1 Equations of Internal Waves in Fluids |

| 1.2 Equations of Ion-Sound Waves in Plasma |

Chapter 2. | Blow-Up of Solutions of Pseudo-Hyperbolic Equations |

| 2.1 Blow-Up of Internal Gravitational Waves |

| 2.2 Blow-Up of Ion-Sound Waves in Plasma |

| 2.3 Blow-Up of Ion-Sound Waves in Plasma with Strong Spatial-Time Dispersion |

Chapter 3. | Nonlinear Dynamical Boundary Conditions |

| 3.1 Blow-Up of Solutions of the Equation of Ion-Sound Waves with Nonlinear Dynamical Boundary Condition |

| 3.2 Blow-Up of Solutions of the Equation of Gravitational-Gyroscopic Waves with Nonlinear Boundary Conditions |

Chapter 4. | Model Systems of Pseudo-Hyperbolic Equations |

| 4.1 System of Equations of Ion-Sound 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 Quasi-Stationary Fields in Crystalline Semiconductors |

| 5.2 Model Equations |

| 5.3 Model Equations for the Function *h(t)* |

Chapter 6. | Blow-Up of Solutions of Nonlocal Sobolev Equations |

| 6.1 Blow-Up of Solutions of an Initial-Boundary-Value Problem for the Nonlinear Nonlocal Benjamin–Bona–Mahony–Burgers Equation with Sources |

| 6.2 Blow-Up of Solutions of the Nonlinear Nonlocal Benjamin–Bona–Mahony–Burgers Wave Equation with a Nonlocal Source |

| 6.3 Blow-Up of Solutions of Nonlocal Dissipative Rosenau–Burgers Equation with a Source |

| 6.4 Blow-Up of Solutions of the Nonlinear Nonlocal Equation of Spin Waves with a Source |

Chapter 7. | Blow-Up of Solutions of Nonlocal Sobolev Systems |

| 7.1 Blow-Up of Solutions of One System of Nonlocal Equations with Sources |

| 7.2 Blow-Up of Solutions of the Nonlinear Nonlocal Oskolkov System with a Source |

Chapter 8. | Blow-Up 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 Blow-Up of Strong Generalized Solutions |

Chapter 9. | Blow-Up of Solutions of Problems with Nonlinear Boundary Conditions |

| 9.1 Blow-Up of Solutions of One Problem with Nonlinear Neumann Boundary condition |

| 9.2 Blow-Up 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 Quasi-Stationary Fields |

| 10.2 Time Dispersion |

| 10.3 Spatial Dispersion |

| 10.4 Nonlinear Factors |

| 10.5 Model Integro-Differential Equations and Sobolev-Type Equations |

Chapter 11. | Blow-Up of Solutions of Wave Integro-Differential Equations of Sobolev Type |

| 11.1 Blow-Up of Solutions of One Equation of Third Order |

| 11.2 Blow-up 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 | Browder–Minty 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 Integro-Differential Inequalities |

| A.11 | Auxiliary Lemmas about Homogeneous Functionals |

| A.12 | Dense Embeddings of Banach Spaces |

| A.13 | Frechet Derivative of the *p*-Laplacian |

Appendix |

Index |

Appendix |

Bibliography |