Asymptotic Behaviors For Solutions Of Viscosity Conservation Laws And Related Problems

In this thesis, we study the L~p-decay rate of the rarefaction wave for scalar conservationlaw with degenerate viscosity, L~p-decay rate toward the rarefaction wave for solutions ofgeneralized KdV-Burgers equation, and asymptotic convergence of the solution for the dampedwave equation with a general boundary data and a non-convex flux in a half space.Under the condition of convex flux, using L~1-estimate derives a L~p-decay rate of therarefaction wave for scalar conservation law with degenerate viscosity. Therefore, the effect ofthe general boundary data on the decay rate is clarified.Under the condition of convex flux and small perturbation for the initial data, usingL~1-estimate andL~-energy method derives anL~p-decay rate of the rarefaction wave forgeneral variable coefficient KdV-Burgers equation with a general boundary data.Successively, we consider the the asymptotic behaviors of solutions for the damped waveequation, whose the boundary data depends on the time variable, and non-convex flux satisfiesthe condtion f"(0)＞0,|f’(0)|＜1. It is proved that the global solutions exist and convergetime-asymptotically to a strong stationary wave and weak rarefaction wave by using anL~2-weighted energy method.