Damping to prevent the blow-up of the Korteweg-de Vries equation

2015/03/30 by Pierre Garnier, Garnier, Pierre
Mathematics · #35B44 #35Q53 #76B03 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B44 #msc:35Q53 #msc:76B03 #msc:76B15

paper · pdf · doi:10.48550/arxiv.1503.08559

arxiv created 2015/03/30 · arxiv updated 2015/03/31

Abstract

We study the behavior of the solution of a generalized damped KdV equation u_t + u_x + u_xxx + u^p u_x + \mathscrL_γ(u)= 0. We first state results on the local well-posedness. Then when p ≥ 4, conditions on \mathscrL_γ are given to prevent the blow-up of the solution. Finally, we numerically build such sequences of damping.

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