Asymptotic Behavior For Solutions Of The Initial-boundary Problems To A Relaxation Model And A Viscoelastic Model

The large time behaviors are studied to the initial-boundary problems of 2x2 nonlinear hyperbolic system of conservation laws with relaxation and 2x2 nonlinear system of viscoelasticity in this thesis.Using an L2 energy method proves that the solutions of the general initial-boundary problem to this relaxation model converges time-asymptotically to a stationary wave or a rarefaction wave or superposition of these two kinds wave for small perturbation.Under the assumptions of non-convexity and non-degeneration, it is proved that the solutions of the initial-boundary problem to this viscoelastic model tend towards the travelling wave solution of the corresponding Cauchy problem time-asymptotically for zero boundary speed and small initial perturbation by a weighted energy method.