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arXiv · 1503.08559

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

Pierre Garnier
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Abstract

We study the behavior of the solution of a generalized damped KdV equation $u_t + u_x + u_{xxx} + u^p u_x + \mathscr{L}_{\gamma}(u)= 0$. We first state results on the local well-posedness. Then when $p \geq 4$, conditions on $\mathscr{L}_{\gamma}$ are given to prevent the blow-up of the solution. Finally, we numerically build such sequences of damping.

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Pierre Garnier. 2015-03-30. Damping to prevent the blow-up of the Korteweg-de Vries equation. https://arxiv.org/abs/1503.08559

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