Global existence and nonexistence of solutions to the Cahn-Hilliard
equation with variable exponent sources
Abstract
This paper deals with a Cahn-Hilliard equation with variable exponent
sources. By using the potential well method, we give some threshold
results on existence and nonexistence of global weak solutions when
initial data with energy less than the potential well depth $d$. In
the former case, we also show the exponential decay properties of energy
functional. We finally obtain some sufficient conditions for the global
existence and non-global existence results with high energy initial
data. The results of this paper extend some recent results of Han (2018)
\cite{Han18} and Zhou (2019)
\cite{Zhou19} to the case of PDEs with variable
exponent sources.