Methods for solving inverse problems in mathematical physics:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
2000
|
| Series: | Pure and applied mathematics
231 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 709 S. |
| ISBN: | 0824719875 |
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MARC
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| 245 | 1 | 0 | |a Methods for solving inverse problems in mathematical physics |c Aleksey I. Prilepko ; Dmitry G. Orlovsky ; Igor A. Vasin |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 2000 | |
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| 650 | 7 | |a Problèmes inversés (Equations différentielles) - Solutions numériques |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Inverse problems (Differential equations) |x Numerical solutions | |
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Record in the Search Index
| _version_ | 1804127361373831168 |
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| adam_text | Titel: Methods for solving inverse problems in mathematical physics
Autor: Prilepko, Aleksej I
Jahr: 2000
Contents
Preface {[{
1 Inverse Problems for Equations of Parabolic Type 1
1.1 Preliminaries 1
1.2 The linear inverse problem: recovering a source term 25
1.3 The linear inverse problem: the Fredholm solvability 41
1.4 The nonlinear coefficient inverse problem:
recovering a coefficient depending on x 54
1.5 The linear inverse problem: recovering the evolution of
a source term 60
2 Inverse Problems for Equations of Hyperbolic Type 71
2.1 Inverse problems for z-hyperbolic systems 71
2.2 Inverse problems for t-hyperbolic systems 88
2.3 Inverse problems for hyperbolic equations
of the second order 106
3 Inverse Problems for Equations of the Elliptic Type 123
3.1 Introduction to inverse problems in potential theory 123
3.2 Necessary and sufficient conditions for the equality of
exterior magnetic potentials 127
3.3 The exterior inverse problem for the volume potential with
variable density for bodies with a star-shaped intersection 139
3.4 Integral stability estimates for the inverse problem
of the exterior potential with constant density 152
3.5 Uniqueness theorems for the harmonic potential
of non-star-shaped bodies with variable density 166
3.6 The exterior contact inverse problem for the magnetic
potential with variable density of constant sign 171
3.7 Integral equation for finding the density of a given body
via its exterior potential 179
3.8 Uniqueness of the inverse problem solution for
the simple layer potential 192
3.9 Stability in inverse problems for the potential of
a simple layer in the space Rn, n 3 197
xi
Contents
4 Inverse Problems in Dynamics of Viscous
Incompressible Fluid 203
4.1 Preliminaries 203
4.2 Nonstationary linearized system of Navier-Stokes
equations: the final overdetermination 209
I 4.3 Nonstationary linearized system of Navier-Stokes
equations: the integral overdetermination 221
4.4 Nonstationary nonlinear system of Navier-Stokes
equations: three-dimensional flow 230
4.5 Nonstationary nonlinear system of Navier-Stokes
equations: two-dimensional flow 248
4.6 Nonstationary nonlinear system of Navier-Stokes
equations: the integral overdetermination 254
4.7 Nonstationary linearized system of Navier-Stokes
equations: adopting a linearization via
recovering a coefficient 266
4.8 Nonstationary linearized system of Navier-Stokes
equations: the combined recovery of two coefficients 281
5 Some Topics from Functional Analysis
and Operator Theory 299
5.1 The basic notions of functional analysis
and operator theory 299
5.2 Linear differential equations
of the first order in Banach spaces 329
5.3 Linear differential equations
of the second order in Banach spaces 342
5.4 Differential equations with
varying operator coefficients 354
5.5 Boundary value problems for elliptic differential
equations of the second order 364
6 Abstract Inverse Problems for First Order Equations
and Their Applications in Mathematical Physics 375
6.1 Equations of mathematical physics and abstract problems 375
6.2 The linear inverse problem with smoothing
overdetermination: the basic elements of the theory 380
6.3 Nonlinear inverse problems with smoothing
overdetermination: solvability 394
6.4 Inverse problems with smoothing overdetermination:
smoothness of solution 406
Contents
xiii
6.5 Inverse problems with singular overdetermination:
semilinear equations with constant operation
in the principal part 414
6.6 Inverse problems with smoothing overdetermination:
quasilinear parabolic equations 438
6.7 Inverse problems with singular overdetermination:
semilinear parabolic equations 449
6.8 Inverse problems with smoothing overdetermination:
semilinear hyperbolic equations 458
6.9 Inverse problems with singular overdetermination:
semilinear hyperbolic equations 469
6.10 Inverse problems with smoothing overdetermination:
semilinear hyperbolic equations and operators
with fixed domain 476
7 Two-Point Inverse Problems for First Order Equations 489
7.1 Two-point inverse problems 489
7.2 Inverse problems with self-adjoint operator
and scalar function 4 501
7.3 Two-point inverse problems in Banach lattices 514
8 Inverse Problems for Equations of Second Order 523
8.1 Cauchy problem for semilinear hyperbolic equations 523
8.2 Two-point inverse problems for equations
of hyperbolic type 537
8.3 Two-point inverse problems for equations
of the elliptic type 557
9 Applications of the Theory of Abstract Inverse Problems
to Partial Differential Equations 575
9.1 Symmetric hyperbolic systems 575
9.2 Second order equations of hyperbolic type 584
9.3 The system of equations from elasticity theory 591
9.4 Equations of heat transfer 597
9.5 Equation of neutron transport 607
9.6 Linearized Bolzman equation 614
9.7 The system of Navier-Stokes equations 628
9.8 The system of Maxwell equations 636
10 Concluding Remarks 645
References
Index ^5
|
| any_adam_object | 1 |
| author | Prilepko, Aleksej I. Orlovsky, Dmitry G. Vasin, Igor A. |
| author_facet | Prilepko, Aleksej I. Orlovsky, Dmitry G. Vasin, Igor A. |
| author_role | aut aut aut |
| author_sort | Prilepko, Aleksej I. |
| author_variant | a i p ai aip d g o dg dgo i a v ia iav |
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| callnumber-subject | QC - Physics |
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| ctrlnum | (OCoLC)41284950 (DE-599)BVBBV012700088 |
| dewey-full | 530.15/535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/535 |
| dewey-search | 530.15/535 |
| dewey-sort | 3530.15 3535 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| isbn | 0824719875 |
| language | English |
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| physical | XIII, 709 S. |
| publishDate | 2000 |
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| publisher | Dekker |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Prilepko, Aleksej I. Verfasser aut Methods for solving inverse problems in mathematical physics Aleksey I. Prilepko ; Dmitry G. Orlovsky ; Igor A. Vasin New York [u.a.] Dekker 2000 XIII, 709 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 231 Física matemática Physique mathématique ram Problemas inversos (Ecuaciones diferenciales) - Soluciones númericas Problèmes inversés (Equations différentielles) - Solutions numériques ram Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Inverses Problem (DE-588)4125161-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Orlovsky, Dmitry G. Verfasser aut Vasin, Igor A. Verfasser aut Pure and applied mathematics 231 (DE-604)BV000001885 231 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008631627&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prilepko, Aleksej I. Orlovsky, Dmitry G. Vasin, Igor A. Methods for solving inverse problems in mathematical physics Pure and applied mathematics Física matemática Physique mathématique ram Problemas inversos (Ecuaciones diferenciales) - Soluciones númericas Problèmes inversés (Equations différentielles) - Solutions numériques ram Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Numerisches Verfahren (DE-588)4128130-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4037952-8 (DE-588)4125161-1 |
| title | Methods for solving inverse problems in mathematical physics |
| title_auth | Methods for solving inverse problems in mathematical physics |
| title_exact_search | Methods for solving inverse problems in mathematical physics |
| title_full | Methods for solving inverse problems in mathematical physics Aleksey I. Prilepko ; Dmitry G. Orlovsky ; Igor A. Vasin |
| title_fullStr | Methods for solving inverse problems in mathematical physics Aleksey I. Prilepko ; Dmitry G. Orlovsky ; Igor A. Vasin |
| title_full_unstemmed | Methods for solving inverse problems in mathematical physics Aleksey I. Prilepko ; Dmitry G. Orlovsky ; Igor A. Vasin |
| title_short | Methods for solving inverse problems in mathematical physics |
| title_sort | methods for solving inverse problems in mathematical physics |
| topic | Física matemática Physique mathématique ram Problemas inversos (Ecuaciones diferenciales) - Soluciones númericas Problèmes inversés (Equations différentielles) - Solutions numériques ram Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Numerisches Verfahren (DE-588)4128130-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Física matemática Physique mathématique Problemas inversos (Ecuaciones diferenciales) - Soluciones númericas Problèmes inversés (Equations différentielles) - Solutions numériques Mathematische Physik Inverse problems (Differential equations) Numerical solutions Mathematical physics Numerisches Verfahren Inverses Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008631627&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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