Global existence and blow-up of weak solutions for a pseudo-parabolic equation with high initial energy

A class of fourth-order hyperbolic equations with strongly damped and nonlinear logarithmic terms

“…therefore, up to a subsequence, by ( 39)-( 42), we could pass to the limit in (43). Moreover, from( 34) and ( 35), we get u(x, 0) = u 0 in H and u t (x, 0) = u 1 in L 2 (Ω).…”

“…In addition, the hyperbolic equation is different from the parabolic equation. The parabolic equation with strong damping term has been extensively studied by many authors, and a large number of results have been obtained [11,20,27,29,37,39,43]. Specially, Chen and Xu [12] studied the initial boundary value problem of infinitely degenerate semilinear pseudo-parabolic equations with logarithmic nonlinear terms, and obtained the global existence, blow up and the asymptotic behavior of the solution.…”

Precise decay rates of global solutions and an explicit upper bound of the blow‐up time to a pseudo‐parabolic equation

“…Throughout this paper, we set here B is the embedding constant in Lemma 2.4. More precisely, d ≥ E 1 in Zhu et al 18 …”

“…In the absence of the strong damping term Δ u t , many complete results such as existence, blow‐up, extinction, and nonextinction have been shown, the interested readers may refer to previous studies 10–13 and the references therein. Although some results on global existence, local existence, blow‐up, and asymptotic behavior of solutions for problem () were obtained in previous studies, 14–18 there are still some unsolved questions (see Questions 1 and 2). In what follows, let us summarize and list some useful results for the sake of simplicity.…”

“…Let us define where the potential depth and In fact, d is positive 18 …”