Multidimensional Inverse and Ill-Posed Problems for Differential Equations
VSP International Science Publishers (Verlag)
978-90-6764-185-2 (ISBN)
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This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interet to researchers in the field of applied mathematics, geophysics and mathematical biology.
Yurii E. Anikonov, Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia.
Part 1 Operator equations and inverse problems: definition of quasimonotonicity, the uniqueness theorem; inverse problems for hyperbolic equations; multidimensional inverse kinematic problems of seismics; on the uniqueness of the solution of the Fredholm and Volterra first-kind integral equations; on the uniqueness of a solution of integral equations of the first kind with entire kernel; existence and uniqueness of a solution to an inverse problem for a parabolic equation; formulas in multidimensional inverse problems for evolution equations. Part 2 Inverse problems for kinetic equations: kinetic equations; an example of an inverse problems for kinetic equation; one-dimensional inverse problems; multidimensional inverse problems; an uniqueness theorem for the solution of an inverse problem for a kinetic equation; the general uniqueness theorem; the effect of the "redundant" equation; problem of separation; differential and integro-differential identities; solution-existence problems; an inverse problem of mathematical biology. Part 3 Geometry of convex surfaces in the large and inverse problems of scattering theory: geometrical question of scattering theory; integral equation of the first kind; uniqueness; existence; stability. Part 4 Integral geometry: inversion formulas; the uniqueness and solvability; some applications; the structure of Riemann spaces and problems of the integral geometry; the solvability of a problem in integral geometry by integration along geodesics.
| Reihe/Serie | Inverse and Ill-Posed Problems Series |
|---|---|
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 410 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 90-6764-185-5 / 9067641855 |
| ISBN-13 | 978-90-6764-185-2 / 9789067641852 |
| Zustand | Neuware |
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