Integral Geometry and Inverse Problems for Hyperbolic Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1974
|
| Series: | Springer Tracts in Natural Philosophy
26 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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. |
| Physical Description: | 1 Online-Ressource (VI, 154 p) |
| ISBN: | 9783642807817 9783642807831 |
| ISSN: | 0081-3877 |
| DOI: | 10.1007/978-3-642-80781-7 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423023 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1974 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642807817 |c Online |9 978-3-642-80781-7 | ||
| 020 | |a 9783642807831 |c Print |9 978-3-642-80783-1 | ||
| 024 | 7 | |a 10.1007/978-3-642-80781-7 |2 doi | |
| 035 | |a (OCoLC)863856914 | ||
| 035 | |a (DE-599)BVBBV042423023 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Romanov, V. G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integral Geometry and Inverse Problems for Hyperbolic Equations |c by V. G. Romanov |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1974 | |
| 300 | |a 1 Online-Ressource (VI, 154 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Springer Tracts in Natural Philosophy |v 26 |x 0081-3877 | |
| 500 | |a 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. | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralgeometrie |0 (DE-588)4161911-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |D s |
| 689 | 0 | 1 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |D s |
| 689 | 1 | 1 | |a Integralgeometrie |0 (DE-588)4161911-0 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Inverses Problem |0 (DE-588)4125161-1 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-80781-7 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858440 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153098263855104 |
|---|---|
| any_adam_object | |
| author | Romanov, V. G. |
| author_facet | Romanov, V. G. |
| author_role | aut |
| author_sort | Romanov, V. G. |
| author_variant | v g r vg vgr |
| building | Verbundindex |
| bvnumber | BV042423023 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863856914 (DE-599)BVBBV042423023 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-80781-7 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03478nmm a2200589zcb4500</leader><controlfield tag="001">BV042423023</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1974 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642807817</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-80781-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642807831</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-80783-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-80781-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863856914</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423023</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Romanov, V. G.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integral Geometry and Inverse Problems for Hyperbolic Equations</subfield><subfield code="c">by V. G. Romanov</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1974</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VI, 154 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Springer Tracts in Natural Philosophy</subfield><subfield code="v">26</subfield><subfield code="x">0081-3877</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Inverses Problem</subfield><subfield code="0">(DE-588)4125161-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hyperbolische Differentialgleichung</subfield><subfield code="0">(DE-588)4131213-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integralgeometrie</subfield><subfield code="0">(DE-588)4161911-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hyperbolische Differentialgleichung</subfield><subfield code="0">(DE-588)4131213-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Hyperbolische Differentialgleichung</subfield><subfield code="0">(DE-588)4131213-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Integralgeometrie</subfield><subfield code="0">(DE-588)4161911-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Inverses Problem</subfield><subfield code="0">(DE-588)4125161-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-80781-7</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858440</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042423023 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642807817 9783642807831 |
| issn | 0081-3877 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858440 |
| oclc_num | 863856914 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VI, 154 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Springer Tracts in Natural Philosophy |
| spelling | Romanov, V. G. Verfasser aut Integral Geometry and Inverse Problems for Hyperbolic Equations by V. G. Romanov Berlin, Heidelberg Springer Berlin Heidelberg 1974 1 Online-Ressource (VI, 154 p) txt rdacontent c rdamedia cr rdacarrier Springer Tracts in Natural Philosophy 26 0081-3877 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. Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Integralgeometrie (DE-588)4161911-0 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 s Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Integralgeometrie (DE-588)4161911-0 s 2\p DE-604 Inverses Problem (DE-588)4125161-1 s 3\p DE-604 https://doi.org/10.1007/978-3-642-80781-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Romanov, V. G. Integral Geometry and Inverse Problems for Hyperbolic Equations Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Inverses Problem (DE-588)4125161-1 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Integralgeometrie (DE-588)4161911-0 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4125161-1 (DE-588)4131213-2 (DE-588)4161911-0 |
| title | Integral Geometry and Inverse Problems for Hyperbolic Equations |
| title_auth | Integral Geometry and Inverse Problems for Hyperbolic Equations |
| title_exact_search | Integral Geometry and Inverse Problems for Hyperbolic Equations |
| title_full | Integral Geometry and Inverse Problems for Hyperbolic Equations by V. G. Romanov |
| title_fullStr | Integral Geometry and Inverse Problems for Hyperbolic Equations by V. G. Romanov |
| title_full_unstemmed | Integral Geometry and Inverse Problems for Hyperbolic Equations by V. G. Romanov |
| title_short | Integral Geometry and Inverse Problems for Hyperbolic Equations |
| title_sort | integral geometry and inverse problems for hyperbolic equations |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Inverses Problem (DE-588)4125161-1 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Integralgeometrie (DE-588)4161911-0 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie Inverses Problem Hyperbolische Differentialgleichung Integralgeometrie |
| url | https://doi.org/10.1007/978-3-642-80781-7 |
| work_keys_str_mv | AT romanovvg integralgeometryandinverseproblemsforhyperbolicequations |