Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations

This article discusses the initial boundary value problem for a class of coupled systems of semi-linear pseudo-parabolic equations on a bounded smooth domain. Global solutions with exponential decay and asymptotic behavior are obtained when the maximal existence time has a lower bound for both low and overcritical energy cases. A sharp condition linking these phenomena is derived, and it is demonstrated that global existence also applies to the case of the potential well family.