I arge-Time Decay of Solutions of the Damped Kawahara Equation on the

We consider an initial–boundary value problem for the damped Kawahara equation ut − uxxxxx + buxxx + aux + uux + g(x)u = 0 on the halfline R+ with the homogeneous boundary conditions. Sufficient conditions on the damping coefficient g(x) for the large-time decay of solutions in L2(R+) without any smallness assumptions on the initial data are established. In contrast to previous results, these conditions do not require the strict positivity of the damping coefficient at +∞. © 2021, Springer Nature Switzerland AG.