Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 46, pp. 1-22.

Title: Existence and nonexistence of global solutions to the Cahn-Hilliard equation with variable exponent sources
       
Authors: Quach V. Chuong (Univ. of Science, Ho Chi Minh City, Vietnam)
         Le C. Nhan (Univ. of Technology and Education, Ho Chi Minh City, Vietnam)
         Le X. Truong (Univ. of Economics Ho Chi Minh city, Ho Chi Minh city, Vietnam)

Abstract:
In this article, we study the existence and nonexistence of global solutions to the
Cahn-Hilliard equation with variable exponent sources and arbitrary initial energy.
We also study the asymptotic behavior of weak solutions.
Our results extend some recent results of Han [11]
to PDEs with variable exponent sources.

Submitted September 4, 2021. Published July 05, 2022.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: Fourth-order parabolic equation; potential well method;
           global solution; variable exponents.