An initial-boundary value probleme that approximate the quarter-plane problem for the Korteweg-de Vries equation.

T. Colin , Marguerite Gisclon (1)

1 LAMA - Laboratoire de Mathématiques

In this paper, we study the initial-boundary-value problem for the Korteweg-de Vries equation. We obtain global smoothing effects that are uniform with respect to the size of the interval. This allows us to show that the solution of the boundary value problem converges, as the size of the interval converges to infinity, towards the solution of the quarter-plane problem. We also propose a simple finite differents scheme for the problem and prove its stability.

Domaines: Equations aux dérivées partielles [math.AP]

T. Colin, Marguerite Gisclon. An initial-boundary value probleme that approximate the quarter-plane problem for the Korteweg-de Vries equation.. Nonlinear Analysis: Theory, Methods and Applications, 2001, 46, pp.869-892. ⟨hal-00380588⟩