Inverse problems for kinetic and other evolution equations /

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Anikonov, I͡U. E. (I͡Uriĭ Evgenʹevich) (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Utrecht : VSP, 2001.
Colección:Inverse and ill-posed problems series.
Temas:
Evolution equations.
Inverse problems (Differential equations)
Équations d'évolution.
Problèmes inverses (Équations différentielles)
SCIENCE > Energy.
SCIENCE > Mechanics > General.
SCIENCE > Physics > General.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Chapter 1. Formulas for solutions and coefficients of kinetic and other equations
  • 1.1. Kinetic equations
  • 1.2. Several formulas for solutions and coefficients of kinetic equations
  • 1.3. Formulas in the inverse problems for kinetic equations with a potential
  • 1.4. Formulas in tomography problems
  • 1.5. Formulas of inverse problems for kinetic equation and integral geometry involving integration along geodesics
  • 1.6. Differential and functional equations of inverse problems for nonlinear equations
  • Chapter 2. Theorems of uniqueness for inverse problems for kinetic equations2.1. Inverse problem for a system of kinetic equations
  • 2.2. Inverse problems for a system of quantum kinetic equations
  • 2.3. On uniqueness of determination of a form by its integrals along geodesics
  • 2.4. Dynamical model of the ethnic system. Formulas in direct and inverse problems
  • Chapter 3. Spherical harmonic method and inverse problem for kinetic equations
  • 3.1. Spherical harmonics method
  • 3.2. Steady-state transfer equation
  • 3.3. Determining the dispersion index in the case of the P1-approximation3.4. Definition of the dispersion index in the case of the P2-approximation
  • 3.5. Reconstruction of the dispersion index and the source function
  • Chapter 4. Inverse problems for evolution equations of determining two coefficients
  • 4.1. Nonlocal boundary-value problems for nonlinear equations and inverse problems of determining two coefficients
  • 4.2. Recurrent formulas on derivatives of solutions
  • 4.3. Integrodifferential equations in inverse problems of determining two coefficients for evolution equations4.4. Inverse problem for a system of Maxwell equations
  • 4.5. Determining two unknown coefficients of the parabolic-type equation
  • 4.6. Inhomogeneous conditions of overdetermination
  • 4.7. Representation of solutions and coefficients of partial differential equations of the second order
  • Chapter 5. Some results of multidimensional inverse problems theory
  • 5.1. Formulas for coefficients in inverse problems for general evolutionary equations
  • 5.2. Formulas in inverse problems for difference-differential equations5.3. Inverse problem for evolutionary equations with degeneration and others
  • 5.4. Group analysis and formulas in inverse problems of mathematical physics
  • 5.5. Uniqueness of the solution of an integral equation of the first kind over real algebras with division of the finite dimension
  • 5.6. Methods of geometry in the inverse seismic problem
  • 5.7. Problems associated with projections of convex bodies onto planes
  • Bibliography

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