The Asymptotic Behavior and Blow-Up Rate of a Solution with a Lower Bound on the Highest Existence Duration for Semi-Linear Pseudo-Parabolic Equations

This note addresses the initial-boundary value problem for a class of semi-linear pseudo-parabolic equations defined on a smooth bounded domain, with an emphasis on determining the asymptotic behavior and blow-up rate of the solution. Our analysis considers both low-initial energy and critical-initial energy cases, with a specific focus on establishing a lower bound on the maximal existence time of the solutions to this problem.