Coefficient Inverse Problems for Parabolic Type Equations and Their Application:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
2001
|
| Schriftenreihe: | Inverse and Ill-Posed Problems Series
25 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Biographical note: Peter G. Danilaev, KazanState TechnicalUniversity, Russia Main description: 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 |
| Beschreibung: | 1 Online-Ressource (III, 115 S.) |
| ISBN: | 9789067643481 9783110940916 9783111829760 |
| DOI: | 10.1515/9783110940916 |
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| 500 | |a Main description: 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 | ||
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| indexdate | 2025-02-19T17:40:31Z |
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| isbn | 9789067643481 9783110940916 9783111829760 |
| language | English |
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| spelling | Danilaev, P. G. Verfasser aut Coefficient Inverse Problems for Parabolic Type Equations and Their Application 2001 1 Online-Ressource (III, 115 S.) txt rdacontent c rdamedia cr rdacarrier Inverse and Ill-Posed Problems Series 25 Biographical note: Peter G. Danilaev, KazanState TechnicalUniversity, Russia Main description: 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 Inverses Problem (DE-588)4125161-1 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 s Inverses Problem (DE-588)4125161-1 s 1\p DE-604 https://doi.org/10.1515/9783110940916 Verlag Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110940916&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Danilaev, P. G. Coefficient Inverse Problems for Parabolic Type Equations and Their Application Inverses Problem (DE-588)4125161-1 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4173245-5 |
| title | Coefficient Inverse Problems for Parabolic Type Equations and Their Application |
| title_auth | Coefficient Inverse Problems for Parabolic Type Equations and Their Application |
| title_exact_search | Coefficient Inverse Problems for Parabolic Type Equations and Their Application |
| title_full | Coefficient Inverse Problems for Parabolic Type Equations and Their Application |
| title_fullStr | Coefficient Inverse Problems for Parabolic Type Equations and Their Application |
| title_full_unstemmed | Coefficient Inverse Problems for Parabolic Type Equations and Their Application |
| title_short | Coefficient Inverse Problems for Parabolic Type Equations and Their Application |
| title_sort | coefficient inverse problems for parabolic type equations and their application |
| topic | Inverses Problem (DE-588)4125161-1 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Inverses Problem Parabolische Differentialgleichung |
| url | https://doi.org/10.1515/9783110940916 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110940916&searchTitles=true |
| work_keys_str_mv | AT danilaevpg coefficientinverseproblemsforparabolictypeequationsandtheirapplication |