Identification problems of wave phenomena : theory and numerics /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Lorenzi, A. (Autor), Kabanikhin, S. I. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Utrecht, the Netherlands : VSP, 1999.
Colección:Inverse and ill-posed problems series.
Temas:
Wave equation.
Waves > Mathematics.
Nonlinear wave equations.
Inverse problems (Differential equations)
Volterra equations.
Number theory.
Équations d'onde.
Ondes > Mathématiques.
Équations d'onde non linéaires.
Problèmes inverses (Équations différentielles)
Équations de Volterra.
Théorie des nombres.
Nonlinear wave equations
Number theory
Volterra equations
Wave equation
Waves > Mathematics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction
  • Chapter 1. Statements of the direct and inverse problems. Examples
  • 1.1. Introduction
  • 1.2. Inverse Problems of Mathematical Physics
  • 1.3. Inverse problem for the wave equation
  • 1.4. The equation of plane waves. The dâ€?Alembert formula
  • 1.5. The Cauchy problem
  • 1.6. The dâ€?Alembert operator with smooth initial data
  • 1.7. The Kirchhoff and Poisson formulae
  • 1.8. Huygens principle
  • 1.9. Time-like and space-like surfaces
  • 1.10. Inverse problems with smooth initial data
  • 1.11. Inverse problem for the acoustic equation
  • Chapter 2. Volterra operator equations2.1. Main definitions
  • 2.2. Local well-posedness
  • 2.3. Well-posedness for sufficiently small data
  • 2.4. Well-posedness in the neighborhood of the exact solution
  • Chapter 3. Inverse problems for Maxwellâ€?s equations
  • 3.1. Introduction
  • 3.2. Reduction of inverse problem for Maxwellâ€?s equations to a Volterra operator equation
  • 3.3. Local well-posedness and global uniqueness
  • 3.4. Well-posedness in the neighborhood of the exact solution
  • Chapter 4. Linearization and Newton-Kantorovich method
  • 4.1. Linearization of Volterra operator equations4.2. he linearized inverse problem for the wave equation
  • 4.3. The Newton-Kantorovich method
  • Chapter 5. The Gelâ€?fand
  • Levitan Method
  • 5.1. Introduction
  • 5.2. Gelâ€?fand-Levitanâ€?s approach to multidimensional inverse problems
  • 5.3. Discrete inverse problems
  • 5.4. Discrete direct problems
  • 5.5. An auxiliary problem
  • 5.6. A necessary condition for the existence of the global solution to the discrete inverse problem
  • 5.7. Sufficient conditions for the existence of the global solution to the discrete inverse problemChapter 6. Regularization
  • 6.1. Introduction
  • 6.2. Volterra regularization
  • Chapter 7. The method of the optimal control
  • 7.1. Introduction
  • 7.2. Discrete inverse problem
  • 7.3. Special representation for the solution to the discrete direct problem
  • 7.4. Uniqueness of the stationary point
  • Chapter 8. Inversion of finite-difference schemes
  • 8.1. Convergence of the method of inversion of finite-difference schemes
  • 8.2. Picard and Caratheodory successive approximationsChapter 9. Strongly ill-posed problems
  • 9.1. A strongly ill-posed problem for the Laplace equation
  • 9.2. Conditional continuous dependence on the data
  • 9.3. Approximate solutions to the Cauchy problem for the Laplace equation
  • 9.4. Approximate solutions to the non-characteristic problem for the multidimensional heat equation
  • 9.5. Existence of solutions satisfying operator inequalities
  • Chapter 10. Identification problems related to first-order scalar semilinear equations

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