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There 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.
Book Synopsis Integral Geometry and Inverse Problems for Hyperbolic Equations by : V. G. Romanov
Download or read book Integral Geometry and Inverse Problems for Hyperbolic Equations written by V. G. Romanov and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: There 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.
Book Synopsis Integral Geometry and Inverse Problems for Hyperbolic Equations by : V. G Romanov
Download or read book Integral Geometry and Inverse Problems for Hyperbolic Equations written by V. G Romanov and published by . This book was released on 1974-07-23 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Geometry and Inverse Problems for Hyperbolic Equations by : Vladimir Gavrilovich Romanov
Download or read book Integral Geometry and Inverse Problems for Hyperbolic Equations written by Vladimir Gavrilovich Romanov and published by Springer. This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
In 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.
Book Synopsis Integral Geometry and Inverse Problems for Kinetic Equations by : Anvar Kh. Amirov
Download or read book Integral Geometry and Inverse Problems for Kinetic Equations written by Anvar Kh. Amirov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 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.
No detailed description available for "Inverse Problems of Mathematical Physics".
Book Synopsis Inverse Problems of Mathematical Physics by : V. G. Romanov
Download or read book Inverse Problems of Mathematical Physics written by V. G. Romanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Inverse Problems of Mathematical Physics".
Book Synopsis Integral geometry and inverse problems for hyperbolic equations (Nekotorye obratnye zadači dlja uravnenij giperboličeskogo tipa, engl.) by : Vladimir G. Romanov
Download or read book Integral geometry and inverse problems for hyperbolic equations (Nekotorye obratnye zadači dlja uravnenij giperboličeskogo tipa, engl.) written by Vladimir G. Romanov and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
Book Synopsis Inverse Problems of Mathematical Physics by : Mikhail M. Lavrent'ev
Download or read book Inverse Problems of Mathematical Physics written by Mikhail M. Lavrent'ev and published by Walter de Gruyter. This book was released on 2012-05-07 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Book Synopsis Inverse Problems by : Alexander G. Ramm
Download or read book Inverse Problems written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.
Book Synopsis Inverse Problems for Partial Differential Equations by : Victor Isakov
Download or read book Inverse Problems for Partial Differential Equations written by Victor Isakov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.
This monograph deals with some inverse problems of mathematical physics. It introduces new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations and the kinetic transport equation.
Book Synopsis Investigation Methods for Inverse Problems by : Vladimir G. Romanov
Download or read book Investigation Methods for Inverse Problems written by Vladimir G. Romanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-10 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with some inverse problems of mathematical physics. It introduces new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations and the kinetic transport equation.
