Nonlinear Stability Of Planar Stationary Wave For Two-dimensional Damped Wave Equation

We investigate the initial-boundary value problem for damped wave equation with a nonlinear convection term in two-dimensional space with two boundaries. For the non-degenerate case, under the condition that its planar stationary wave is increasing and the initial-boundary perturbation is small, we use the energy method to obtain the global existence and uniqueness of solution and convergence rate(both algebraic and exponential) of solution toward the planar stationary wave for such an initial-boundary value problem.