Asymptotic Behaviors For Solutions Of Scalar Conservation Law With Degenerate Viscosity And Generalized KdV-Burgers Equation

In this thesis, we study the convergence rate toward the rarefaction wave for solutions of scalar conservation law with degenerate viscosity and asymptotic convergence of the solution to generalized KdV-Burgers equation with a general boundary data in a half space.Under the condition that the flux function is convex and u_< u+, using L1-estimate derives an L2-decay rate toward the rarefaction wave for solutions of scalar conservation law with degenerate viscosity. From this decay rate estimate, the effect of the general boundary data on the decay rate is clarified.Successively, we consider the asymptotic behavior of solutions to generalized KdV-Burgers equation, whose the boundary data depends on the time variable and convex-flux f satisfies the certain growth condition |f"(u)|≤C(1+|u|). By using an L2-energy method and a technique of modifying boundary data, it is proved that the time global solution exists and converges time-asymptotically to the strong rarefaction wave for the large initial-boundary disturbance.