## Differential and Integral Equations

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

Jardel Morais Pereira

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 9, Number 4 (1996), 849-863.

Dates
First available in Project Euclid: 7 May 2013

https://projecteuclid.org/euclid.die/1367969891

Mathematical Reviews number (MathSciNet)
MR1401441

Zentralblatt MATH identifier
0848.35100

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35B35: Stability 76B35

#### Citation

Pereira, Jardel Morais. Stability of multidimensional traveling waves for a Benjamin-Bona-Mahony type equation. Differential Integral Equations 9 (1996), no. 4, 849--863. https://projecteuclid.org/euclid.die/1367969891