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arXiv · 1402.5009

Long-time behavior of solutions of a BBM equation with generalized damping

Jean-Paul Chehab·Pierre Garnier·Youcef Mammeri
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Abstract

We study the long-time behavior of the solution of a damped BBM equation $u_t + u_x - u_{xxt} + uu_x + \mathscr{L}_{\gamma}(u) = 0$. The proposed dampings $\mathscr{L}_{\gamma}$ generalize standards ones, as parabolic ($\mathscr{L}_{\gamma}(u)=-\Delta u$) or weak damping ($\mathscr{L}_{\gamma}(u)=\gamma u$) and allows us to consider a greater range. After establish the local well-posedness in the energy space, we investigate some numerical properties.

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Jean-Paul Chehab, Pierre Garnier, Youcef Mammeri. 2014-02-20. Long-time behavior of solutions of a BBM equation with generalized damping. https://arxiv.org/abs/1402.5009

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