Coefficient Inverse Problems for Parabolic Type Equations and Their Application
Seiten
2001
|
1. Reprint 2014
De Gruyter (Verlag)
978-3-11-036401-9 (ISBN)
De Gruyter (Verlag)
978-3-11-036401-9 (ISBN)
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
As a rule, many practical problems are studied in a situation when the input data are incomplete. For example, this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if it contains the unknown thermal conductivity coefficient. Such situations arising in physical problems motivated the appearance of the present work. In this monographthe author considers numerical solutions of the quasi-inversion problems, to which the solution of the original coefficient inverse problems are reduced. Underground fluid dynamics is taken as a field of practical use of coefficient inverse problems. The significance of these problems for this application domain consists in the possibility to determine the physical fields of parameters that characterize the filtration properties of porous media (oil strata). This provides the possibility of predicting the conditions of oil-field development and the effects of the exploitation. The research carried out by the author showed that the quasi-inversion method can be applied also for solution of "interior coefficient inverse problems" by reducing them to the problem of continuation of a solution to a parabolic equation. This reduction is based on the results of the proofs of the uniqueness theorems for solutions of the corresponding coefficient inverse problems.
As a rule, many practical problems are studied in a situation when the input data are incomplete. For example, this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if it contains the unknown thermal conductivity coefficient. Such situations arising in physical problems motivated the appearance of the present work. In this monographthe author considers numerical solutions of the quasi-inversion problems, to which the solution of the original coefficient inverse problems are reduced. Underground fluid dynamics is taken as a field of practical use of coefficient inverse problems. The significance of these problems for this application domain consists in the possibility to determine the physical fields of parameters that characterize the filtration properties of porous media (oil strata). This provides the possibility of predicting the conditions of oil-field development and the effects of the exploitation. The research carried out by the author showed that the quasi-inversion method can be applied also for solution of "interior coefficient inverse problems" by reducing them to the problem of continuation of a solution to a parabolic equation. This reduction is based on the results of the proofs of the uniqueness theorems for solutions of the corresponding coefficient inverse problems.
Peter G. Danilaev, KazanState TechnicalUniversity, Russia.
| Erscheint lt. Verlag | 18.6.2001 |
|---|---|
| Reihe/Serie | Inverse and Ill-Posed Problems Series ; 25 |
| Zusatzinfo | Num. figs. |
| Verlagsort | Berlin/Boston |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Gewicht | 345 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie | |
| Schlagworte | coefficient inverse problems • Identifikationsverfahren • Inverses Problem • numerical solutions • Numerical Solutions; Quasi-inversion Problems; Coefficient Inverse Problems; Underground Fluid Dynamics; Parabolic Equations • Parabolic equations • Parabolische Differentialgleichung • Quasi-inversion Problems • Underground Fluid Dynamics |
| ISBN-10 | 3-11-036401-8 / 3110364018 |
| ISBN-13 | 978-3-11-036401-9 / 9783110364019 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 83,90
