Abstract
In this paper, we investigate the initial boundary value problems for a class of quasilinearhyperbolic-parabolic coupled systems including the equations of radiation hydrodynamics and of visco-elasticity as special cases. Using the energy method and the continuation argument, we have provedthe global existence and uniqueness of smooth solutions and the exponential decay of solutions as t→+∞ provided that the initial data is sufficiently small. Then we apply the obtained results to thecorresponding initial boundary value problems for the systems of radiation dydrodynamics and ofviscoelasticity.
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