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For the hyperbolic system of quasilinear first-order partial differentialequations, linearizable by hodograph transformation, the conservation laws areused to solve the Cauchy problem. The equivalence of the initial problem forquasilinear system and the problem for conservation laws system permits toconstruct the characteristic lines in domains, where Jacobian of hodographtransformations is equal to zero. Moreover, the conservation laws give allsolutions of the linearized system. Some examples from the gas dynamics andtheory of plasticity are considered.

Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity