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In this paper, we reduce the nonlinear elastic dynamic system, with a polyconvex stored energy function, to a first order symmetric hyperbolic system in the form of conservation laws.
A class of semilinear hyperbolic Volterra integrodifferential equations in Hilbert spaces is considered. The main results in this paper are the global existence of solutions to the initial problem of… (More)
The paper discusses the asymptotic behaviour of weak solutions u ( t, x ), as t → ∞, to the boundary value problem for one-dimensional viscoelastic equations with singular memory. The changes of… (More)
The authors deal with the Cauchy problem with small initial data for the nonlinear elastodynamic system. The almost global existence of solution to this problem is proved in a simpler way and a lower… (More)
In this paper, we show the existence of nontrivial travelling wave solutions, which propagating speeds are between ones determined by the equilibrium and instantaneous elastic tensor, respectively,… (More)