Stability of multidimensional traveling waves for a Benjamin-Bona-Mahony type equation. (English) Zbl 0848.35100

Pereira, Jardel Morais

Differ. Integral Equ. 9, No. 4, 849-863 (1996).

Summary: We show that for a convenient choice of the nonlinear map \(a(u)\) the equation \[ u_t+ \text{div}(a(u))- \Delta u_t= 0 \] has traveling waves solution \(\phi_c(x- \vec ct)\), where \(\vec c= (c,\dots, c)\in \mathbb{R}^n\). For \(c\) varying in a suitable interval we show that these traveling waves are stable.

MSC:

35Q35	PDEs in connection with fluid mechanics
35B35	Stability in context of PDEs
76B15	Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M35	Stochastic analysis applied to problems in fluid mechanics

Keywords:

existence and stability of traveling waves; generalized Benjamin-Bona-Mahony equation; traveling waves solution