Integral geometry and inverse problems for hyperbolic equations (Nekotorye obratnye zadači dlja uravnenij giperboličeskogo tipa, engl.)
Author: Vladimir G. Romanov
Publisher:
Published: 1974
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Vladimir G. Romanov
Publisher:
Published: 1974
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKAuthor: V. G. Romanov
Publisher: Springer Science & Business Media
Published: 2013-04-09
Total Pages: 160
ISBN-13: 364280781X
DOWNLOAD EBOOKThere are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solution on the data is retained but it is interpreted differently. It is required that solutions depend continuously only on that data which does not take the solutions out of M.
Author: V. G Romanov
Publisher:
Published: 1974-07-23
Total Pages: 164
ISBN-13: 9783642807824
DOWNLOAD EBOOKAuthor: Vladimir Gavrilovich Romanov
Publisher: Springer
Published: 1974
Total Pages: 0
ISBN-13: 9780387064291
DOWNLOAD EBOOKAuthor: Sergey I. Kabanikhin
Publisher: Walter de Gruyter
Published: 2013-04-09
Total Pages: 188
ISBN-13: 3110960710
DOWNLOAD EBOOKThe authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.
Author: Anvar Kh. Amirov
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2014-07-24
Total Pages: 212
ISBN-13: 3110940949
DOWNLOAD EBOOKIn this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another considered subject is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of solutions to this problem for a class of quasilinear hyperbolic equations. A class of multidimensional inverse problems associated with problems of integral geometry and the inverse problem for the quantum kinetic equations are also included.