| This thesis is concerned with convergence rate toward the rarefaction waves of the solutions for scalar viscous conservation laws and asymptotic behaviors of solutions for generalized BBM-Burgers equation with a general boundary data in a half space.Under the condition that the flux function is convex, using an L~2 energy method and an L~1 estimate derives a convergence rate in L~2 norm toward the rarefaction waves of the solutions for scalar viscous conservation laws in a half space. From this convergence rate estimate, the effect of the general boundary data on the convergence rate is clarified.For the generalized BBM-Burgers equation with a general boundary data in a half space, it is showed that its global solution exists and converges time-asymptotically to a weak stationary wave or the linear superposition of a weak stationary wave and a weak rarefaction wave for non-convex flux function and small initial-boundary disturbance by an L~2 weighted energy method. |
