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Cover Korpusov M.O., Ovchinnikov A.V. Blow-Up of Solutions of Model Nonlinear Equations of Mathematical Physics
Id: 173543
 
69.9 EUR

Blow-Up of Solutions of Model Nonlinear Equations of Mathematical Physics

URSS. 488 pp. (English). Paperback. ISBN 978-5-396-00558-7.

 Summary

The present monography is dedicated to a fashionable trend in nonlinear analysis --- the theories of blow-up of solutions for final time. In this book nonlinear Sobolev type equations are systematically studied. The book will be interesting both to experts in the field of nonlinear analysis and to students and post-graduate students of the corresponding specialties.


 Contents

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.1Sobolev Spaces Ws,p(Omega)Ws,p0(Omega), and Ws,p(Gamma)
 A.2Weak and ast -Weak Convergence
 A.3Chain Rule for Frechet Derivatives
 A.4Caratheodori Functions. Nemytsky Operators. Krasnosel'sky Theorem
 A.5Compact Continuous Operators and Completely Continuous Operators
 A.6Compactness Lemma of J.-L.Lions
 A.7Browder--Minty Theorem
 A.8On the System of Ordinary Differential Equations in the Galerkin Method
 A.9Two Equivalent Definitions of a Weak Solution in the Sense of L2(0, T; B)
 A.10Basic Integro-Differential Inequalities
 A.11Auxiliary Lemmas about Homogeneous Functionals
 A.12Dense Embeddings of Banach Spaces
 A.13Frechet Derivative of the p-Laplacian
Appendix
Index
Appendix
Bibliography

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