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.
Categories: math.AP math.NA