Conservation laws, hodograph transformation and boundary value problems of plane plasticity. (English) Zbl 1270.35309

Senashov, Sergey I.; Yakhno, Alexander

SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 071, 16 p. (2012).

Summary: For hyperbolic systems 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 the Jacobian of the 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.

MSC:

35L65	Hyperbolic conservation laws
58J45	Hyperbolic equations on manifolds
74G10	Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35L60	First-order nonlinear hyperbolic equations

Keywords:

Riemann method; quasilinear equations; characteristic lines; gas dynamics