Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity
For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for quasilinear system and the problem for conservation laws system permit...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148678 |
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| Zitieren: | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity / S.I. Senashov, A. Yakhno // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862576145176723456 |
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| author | Senashov, S.I. Yakhno, A. |
| author_facet | Senashov, S.I. Yakhno, A. |
| citation_txt | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity / S.I. Senashov, A. Yakhno // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for quasilinear system and the problem for conservation laws system permits to construct the characteristic lines in domains, where Jacobian of hodograph transformations is equal to zero. Moreover, the conservation laws give all solutions of the linearized system. Some examples from the gas dynamics and theory of plasticity are considered.
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| first_indexed | 2025-11-26T14:35:54Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148678 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T14:35:54Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Senashov, S.I. Yakhno, A. 2019-02-18T17:50:49Z 2019-02-18T17:50:49Z 2012 Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity / S.I. Senashov, A. Yakhno // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35L65; 58J45; 74G10 DOI: http://dx.doi.org/10.3842/SIGMA.2012.071 https://nasplib.isofts.kiev.ua/handle/123456789/148678 For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for quasilinear system and the problem for conservation laws system permits to construct the characteristic lines in domains, where Jacobian of hodograph transformations is equal to zero. Moreover, the conservation laws give all solutions of the linearized system. Some examples from the gas dynamics and theory of plasticity are considered. This paper is a contribution to the Special Issue “Geometrical Methods in Mathematical Physics”. The full collection is available at http://www.emis.de/journals/SIGMA/GMMP2012.html.
 We would like to express our gratitude to unknown referees for useful corrections. This work
 was partially supported by PRO-SNI (UdeG). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity Article published earlier |
| spellingShingle | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity Senashov, S.I. Yakhno, A. |
| title | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity |
| title_full | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity |
| title_fullStr | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity |
| title_full_unstemmed | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity |
| title_short | Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity |
| title_sort | conservation laws, hodograph transformation and boundary value problems of plane plasticity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148678 |
| work_keys_str_mv | AT senashovsi conservationlawshodographtransformationandboundaryvalueproblemsofplaneplasticity AT yakhnoa conservationlawshodographtransformationandboundaryvalueproblemsofplaneplasticity |