Investigation methods for inverse problems /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Romanov, V. G. (Vladimir Gavrilovich) (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Utrecht ; Boston : VSP, 2002.
Colección:Inverse and ill-posed problems series.
Temas:
Inverse problems (Differential equations) > Numerical solutions.
Mathematical physics.
Problèmes inverses (Équations différentielles) > Solutions numériques.
Physique mathématique.
Inverse problems (Differential equations) > Numerical solutions
Mathematical physics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface
  • 1 Introduction
  • 1.1 One-dimensional inverse kinematics problem
  • 1.2 Inverse dynamical problem for a string
  • 1.3 Inverse problems for a layered medium
  • 2 Ray statements of inverse problems
  • 2.1 Posing of the inverse problems
  • 2.2 Asymptotic expansion
  • 2.2.1 Asymptotic expansion of the solution
  • 2.2.2 Reduction of the inverse problem
  • 2.2.3 Construction of Ï?(x, y)
  • 2.2.4 Proof of the expansion in the odd-dimensional case
  • 2.2.5 Proof of the expansion in the even-dimensional case
  • 2.2.6 Proof of the auxiliary lemma
  • 2.3 Uniqueness theorems for the inverse problem2.3.1 A proof of the stability estimate for the integral geometry problem
  • 2.3.2 Uniqueness theorem for the integral geometry problem related to a vector field
  • 2.3.3 Proof of the uniqueness theorem for inverse kinematics problem
  • 2.3.4 The wave equation with an attenuation
  • 2.3.5 Concluding remarks
  • 2.4 Inverse problems related to a local heterogeneity
  • 3 Local solvability of some inverse problems
  • 3.1 Banachâ€?s spaces of analytic functions
  • 3.2 Determining coefficients of the lower terms
  • 3.2.1 Determining a coefficient of the lower term3.2.2 Determining an attenuation coefficient
  • 3.3 Determining the speed of the sound
  • 3.4 A regularization method for solving an inverse problem
  • 3.4.1 Theorems related to the system of integro-differential equations
  • 3.4.2 Estimates of a solution to the algebraic equations
  • 3.4.3 Convergence the approximate solution to the exact one
  • 4 Inverse problems with single measurements
  • 4.1 Determining coefficient of the lowest term
  • 4.1.1 Statement of the problem and stability estimates
  • 4.1.2 Proof of the stability theorems4.1.3 Proof of Lemma 4.1.3
  • 4.1.4 Proof of Lemma 4.1.4
  • 4.2 Determining coefficients under first derivatives
  • 4.3 Determining the speed of sound in the wave equation
  • 4.3.1 Formulation of the problem and a stability estimate of the solution
  • 4.3.2 Proof of Theorem 4.3.1
  • 4.3.3 Proof of Lemma 4.3.5
  • 4.3.4 Proof of Lemma 4.3.6
  • 4.3.5 Proof of the inequality (4.3.24)
  • 4.4 Case of a point source
  • 4.4.1 Formulations of the problem and results
  • 4.4.2 Proofs of the stability theorems
  • 4.4.3 Properties of a solution to problem (4.4.1)4.4.4 Proof of Lemma 4.4.3
  • 4.4.5 Proof of Lemma 4.4.4
  • 5 Stability estimates related to inverse problems for the transport equation
  • 5.1 The problem of determining the relaxation and a density of inner sources
  • 5.1.1 Statement of basic and auxiliary problems
  • 5.1.2 The basic results
  • 5.1.3 Proof of Theorem 5.1.1
  • 5.1.4 Proof of the auxiliary lemmas
  • 5.2 A stability estimate in the problem of determining the dispersion index and relaxation in 2D
  • 5.2.1 Statement of the problem and the basic results

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