Volume no :28, Issue no: 1, July

Journal of Mathematical Sciences: Advances and Applications

NONLINEAR STABILITY OF PLANAR STATIONARY WAVES FOR DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION TERM IN 2-DIMENSIONAL SPACE WITH TWO BOUNDARIES

Author's: Quanguang Tan
Pages: [61] - [84]
Received Date: April 9, 2014
Submitted by:

Abstract

We investigate the nonlinear stability of increasing planar stationary wave of initial-boundary value problem for damped wave equation with nonlinear convection term in 2-dimensional space with two boundaries. For the non-degenerate case, under the smallness conditions on the initial-boundary perturbation, we use the standard energy method to obtain the global existence of solution and the algebraic convergence rate of solutions toward the planar stationary waves for such an initial-boundary value problem.

Keywords

damped wave equation, two boundaries, planar stationary wave, energy method, decay rate.