Stability of multidimensional traveling waves for a Benjamin-Bona-Mahony type equation

Abstract

In this paper we show that for a convenient choice of the nonlinear map $a(u)$ the equation $u_t + \div (a (u)) - \Delta u_t = 0$ has traveling waves solution $\phi_c (x - \overrightarrow{c} t)$, where $\overrightarrow{c} = (c,\ldots, c)\in\mathbb{R}^n$. For $c$ varying in a suitable interval we show that these traveling waves are stable.