Long-time behavior of solutions of a BBM equation with generalized   damping
  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. 
Jean-Paul Chehab (LAMFA), Pierre Garnier (LAMFA), Youcef Mammeri   (LAMFA)
math.AP math.NA