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Conservation laws, hodograph transformation and boundary value problems of plane plasticity. (English) Zbl 1270.35309
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:
35L65Conservation laws
58J45Hyperbolic partial differential equations on manifolds
74G10Analytic approximation of solutions for equilibrium problems in solid mechanics
35L60Nonlinear first-order hyperbolic equations