Abstract
In this paper, the authors investigate the existence and uniqueness of weak solutions of the initial and boundary value problem for a fourth-order pseudo-parabolic equation with variable exponents of non-linearity. Finally, the authors also obtain a long-time behaviour of weak solutions.
Acknowledgments
The authors would like to thank referees for his/her valuable suggestions and for providing the references S.Antontsev, S.Shmarev [Citation27] and M. M. Porzio [Citation28].
Notes
1 Supported by NSFC (11271154) and by Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education and by the 985 program of Jilin University.