
SIGMA 8 (2012), 071, 16 pages arXiv:1210.3673
https://doi.org/10.3842/SIGMA.2012.071
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”
Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity
Sergey I. Senashov ^{a} and Alexander Yakhno ^{b}
^{a)} Siberian State Aerospace University, Krasnoyarsk, Russia
^{b)} Departamento de Matemáticas, CUCEI, Universidad de Guadalajara, 44430, Mexico
Received April 18, 2012, in final form September 29, 2012; Published online October 13, 2012
Abstract
For the hyperbolic system of quasilinear firstorder 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.
Key words:
conservation laws; hodograph transformation; Riemann method; plane plasticity; boundary value problem.
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