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

• Published in: Journal of mathematical analysis and applications Vol. 506; no. 2; p. 125719
• Main Authors: Tran, Quang-Minh, Vu, Thi-Thi
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15-02-2022
• Subjects: Asymptotic behavior; Blow-up rate; Coupled pseudo-parabolic systems; Finite time blow-up; Global existence; Lifespan; Coupled pseudo-parabolic systems; Global existence; Lifespan; Blow-up rate; Asymptotic behavior; Finite time blow-up
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2021.125719

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.