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- We consider the initial boundary value problem for the system of quasilinear differential equations which describe the one-dimensional motion of a thermoviscoelastic body of the Voigt type. We construct a new nonlinear difference scheme for it.We derive the set of global a priori estimates for the solutions of the difference scheme, prove the existence of solutions, and establish the convergence of the difference scheme to a generalized solution of the problem.

Difference scheme for the system of equations of one-dimensional dynamics of a nonlinear thermoviscoelastic body of the Voigt type