Asymptotic Stability Of Planar Stationary Waves For Two Dimensional Scalar Viscous Conservation Laws

This thesis is concerned with the asymptotic stability of planar stationary wave for general initial-boundary value problem of scalar viscous conservation laws with two boundaries in two dimensional space. Under the condition of large perturbation on initial-boundary data, by virtue of an elementary energy method, it is proved that its global solution exists and is unique and converges toward a strong planar stationary wave for such an initial-boundary value problem. Moreover, an exponential and algebraic convergence rates of the solution toward the planar stationary wave are also obtained for this initial-boundary value problem.