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Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity
Інший ID:
2010 Mathematics Subject Classification: 35L65; 58J45; 74G10
DOI: http://dx.doi.org/10.3842/SIGMA.2012.071
DOI: http://dx.doi.org/10.3842/SIGMA.2012.071
Посилання:
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.
Підтримка:
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).
Дата:
2012
Переглядів:
638
Завантажень:
306
Анотація:
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.
