Open AccessDynamics of solutions to a semilinear plate equation with memory
Author(s) -
JinXing Liu,
Xiongrui Wang,
Jun Zhou,
Xu Liu
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021137
Subject(s) - bounded function , ordinary differential equation , mathematics , uniqueness , domain (mathematical analysis) , initial value problem , dynamics (music) , upper and lower bounds , mathematical analysis , pure mathematics , differential equation , physics , acoustics
In this paper we consider an initial-boundary value problem of a semilinear regularity-loss-type plate equation with memory in a bounded domain of \begin{document}$ \mathbb{R}^n $\end{document} ( \begin{document}$ n = 1,2,\cdots $\end{document} ). By using the Faedo-Galërkin method and some theories of ordinary differential equations, we obtain the local existence and uniqueness of weak solutions. Then, we study the dynamics of the weak solutions, such as global existence and finite time blow-up, by energy estimation and some ordinary differential inequalities. Moreover, the upper bound of blow-up time for the blow-up solutions is also considered.