GLOBAL SOLUTIONS AND APPLICATIONS TO A CLASS OF QUASILINEAR HYPERBOLICPARABOLIC COUPLED SYSTEMS

【摘要】 <正> 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.更多还原

【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.更多还原