We consider the initial value problem for nonlinear partial differential equations describing the motion of inhomogeneous and anisotropic hyperelastic medium. We proved the theorem about existance (local in time) and uniqueness a smooth solution to this initial value problem. In order to do it, we applied the modified Sommerfeld method to convert the considered initial value to a first order quasilinear symmetric hyperbolic system. Next, we proved the blow-up in the finite time of the solution above mentional initial problem under the some assumption about the stored energy function of the hyperelastic matrials. [References: 3]
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