Stability of Traveling Waves to a Burgers Equation with 2nd-Order Nonlinear Diffusion

Abstract

We are interested in the study of asymptotic stability for Burgers equation with second-order nonlinear diffusion. We first transform the original equation by the ansatz transformation to establish the existence of traveling wave. We further employ the energy estimate under small perturbation and arbitrary wave amplitude. This energy estimate is then used to establish the stability.

Keywords

• stability
• arbitrary wave amplitude
• small perturbation
• energy estimate