The global existence and time-decay for the solutions of the fractional pseudo-parabolic equation

We consider the Cauchy problem of fractional pseudo-parabolic equation on the whole space R-n,n >= 1. Here, the fractional order alpha is related to the diffusion-type source term behaving as the usual diffusion term on the high frequency part. It has a feature of regularity-gain and regularity-loss for alpha > 1 and 0 < alpha < 1, respectively. We establish the global existence and time-decay rates for small-amplitude solutions to the Cauchy problem for alpha > 0. In the case that 0 < alpha < 1, we introduce the time-weighted energy method to overcome the weakly dissipative property of the equation. (C) 2017 Elsevier Ltd. All rights reserved.