Some sharp results about the global existence and blowup of solutions to a class of coupled pseudo-parabolic equations

In this paper, we investigate an initial boundary value problem to a class of system pseudo-parabolic equations with power type source terms in low dimensional. By introducing a family of potential wells we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence, blow-up phenomenon of weak solutions for the subcritical, critical and supercritical initial energy cases respectively. Furthermore, we study the decay rates for the global solutions and lifespan, blow-up rates of the blow-up solutions on some special cases. (c) 2021 Elsevier Inc. All rights reserved.