Global solutions of a fractional semilinear pseudo-parabolic equation with nonlocal source

Abstract

In this paper, the initial boundary value problem for a fractional nonlocal semilinear pseudo-parabolic equation is established. Firstly, we get the local solution by the standard Galerkin method and the priori estimates. Next, by applying potential well argument, the existence and uniqueness of the global solution are proved for initial energy $J\left(u_0\right)\le d$.

Keywords:

• Fractional semilinear pseudo-parabolic equation
• boundary value problems
• nonlocal source
• global solution
• potential well

2020 Mathematics Subject Classifications:

• 35A01
• 35A02
• 35K7

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11271141) and the Chongqing Science and Technology Commission (cstc2018jcyjAX0787).