Inverse Stefan Problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1997
|
| Series: | Mathematics and Its Applications
412 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In this monograph the theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in regions with free boundaries are developed. The study of this new class of ill-posed problems is motivated by the needs of the modeling and control of nonlinear processes with phase transitions in thermophysics and mechanics of continuous media. Inverse Stefan problems are important for the perfection of technologies both in high temperature processes (e.g., metallurgy, the aircraft industry, astronautics and power engineering) and in hydrology, exploitation of oil-gas fields, etc. The proposed book will complete a gap in these subjects in the preceding researches of ill-posed problems. It contains the new theoretical and applied studies of a wide class of inverse Stefan problems. The statements of such problems on the determination of boundary functions and coefficients of the equation are considered for different types of additional information about their solution. The variational method of obtaining stable approximate solutions is proposed and established. It is implemented by an efficient computational scheme of descriptive regularization. This algorithm utilizes a priori knowledge of the qualitative structure of the sought solution and ensures a substantial saving in computational costs. It is tested on model and applied problems in nonlinear thermophysics. In particular, the results of calculations for important applications in continuous casting of ingots and in the melting of a plate with the help of laser technology are presented |
| Physical Description: | 1 Online-Ressource (VIII, 250 p) |
| ISBN: | 9789401154888 9789401063098 |
| DOI: | 10.1007/978-94-011-5488-8 |
Staff View
MARC
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| 500 | |a In this monograph the theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in regions with free boundaries are developed. The study of this new class of ill-posed problems is motivated by the needs of the modeling and control of nonlinear processes with phase transitions in thermophysics and mechanics of continuous media. Inverse Stefan problems are important for the perfection of technologies both in high temperature processes (e.g., metallurgy, the aircraft industry, astronautics and power engineering) and in hydrology, exploitation of oil-gas fields, etc. The proposed book will complete a gap in these subjects in the preceding researches of ill-posed problems. It contains the new theoretical and applied studies of a wide class of inverse Stefan problems. The statements of such problems on the determination of boundary functions and coefficients of the equation are considered for different types of additional information about their solution. The variational method of obtaining stable approximate solutions is proposed and established. It is implemented by an efficient computational scheme of descriptive regularization. This algorithm utilizes a priori knowledge of the qualitative structure of the sought solution and ensures a substantial saving in computational costs. It is tested on model and applied problems in nonlinear thermophysics. In particular, the results of calculations for important applications in continuous casting of ingots and in the melting of a plate with the help of laser technology are presented | ||
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| isbn | 9789401154888 9789401063098 |
| language | English |
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| spelling | Golʹdman, Natalija Lʹvovna Verfasser (DE-588)1056095113 aut Inverse Stefan Problems by N. L. Gol'dman Dordrecht Springer Netherlands 1997 1 Online-Ressource (VIII, 250 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 412 In this monograph the theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in regions with free boundaries are developed. The study of this new class of ill-posed problems is motivated by the needs of the modeling and control of nonlinear processes with phase transitions in thermophysics and mechanics of continuous media. Inverse Stefan problems are important for the perfection of technologies both in high temperature processes (e.g., metallurgy, the aircraft industry, astronautics and power engineering) and in hydrology, exploitation of oil-gas fields, etc. The proposed book will complete a gap in these subjects in the preceding researches of ill-posed problems. It contains the new theoretical and applied studies of a wide class of inverse Stefan problems. The statements of such problems on the determination of boundary functions and coefficients of the equation are considered for different types of additional information about their solution. The variational method of obtaining stable approximate solutions is proposed and established. It is implemented by an efficient computational scheme of descriptive regularization. This algorithm utilizes a priori knowledge of the qualitative structure of the sought solution and ensures a substantial saving in computational costs. It is tested on model and applied problems in nonlinear thermophysics. In particular, the results of calculations for important applications in continuous casting of ingots and in the melting of a plate with the help of laser technology are presented Mathematics Differential equations, partial Computer science / Mathematics Surfaces (Physics) Partial Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Characterization and Evaluation of Materials Informatik Mathematik Inverses Problem (DE-588)4125161-1 gnd rswk-swf Stefan-Problem (DE-588)4183000-3 gnd rswk-swf Stefan-Problem (DE-588)4183000-3 s Inverses Problem (DE-588)4125161-1 s 1\p DE-604 Mathematics and Its Applications 412 (DE-604)BV008163334 412 https://doi.org/10.1007/978-94-011-5488-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Golʹdman, Natalija Lʹvovna Inverse Stefan Problems Mathematics and Its Applications Mathematics Differential equations, partial Computer science / Mathematics Surfaces (Physics) Partial Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Characterization and Evaluation of Materials Informatik Mathematik Inverses Problem (DE-588)4125161-1 gnd Stefan-Problem (DE-588)4183000-3 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4183000-3 |
| title | Inverse Stefan Problems |
| title_auth | Inverse Stefan Problems |
| title_exact_search | Inverse Stefan Problems |
| title_full | Inverse Stefan Problems by N. L. Gol'dman |
| title_fullStr | Inverse Stefan Problems by N. L. Gol'dman |
| title_full_unstemmed | Inverse Stefan Problems by N. L. Gol'dman |
| title_short | Inverse Stefan Problems |
| title_sort | inverse stefan problems |
| topic | Mathematics Differential equations, partial Computer science / Mathematics Surfaces (Physics) Partial Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Characterization and Evaluation of Materials Informatik Mathematik Inverses Problem (DE-588)4125161-1 gnd Stefan-Problem (DE-588)4183000-3 gnd |
| topic_facet | Mathematics Differential equations, partial Computer science / Mathematics Surfaces (Physics) Partial Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Mathematical Modeling and Industrial Mathematics Characterization and Evaluation of Materials Informatik Mathematik Inverses Problem Stefan-Problem |
| url | https://doi.org/10.1007/978-94-011-5488-8 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT golʹdmannatalijalʹvovna inversestefanproblems |