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Long-time behavior for competition-diffusion systems via viscosity comparison
Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation
| 1. | Laboratoire de Mathématiques, Université Paris-Sud, 91405 Orsay, France |
$(1-\partial^2_x)u_t+(u+u^2)_x=0.$
We prove that a solution initially close to a solitary wave, once conveniently translated, converges weakly in $H^1(\mathbb R)$, as time goes to infinity, to a possibly different solitary wave. The proof is based on a Liouville type theorem for the flow close to the solitary waves, and makes an extensive use of a monotonicity property.
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