Weak solutions for a high-order pseudo-parabolic equation with variable exponents

¹Supported 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.

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.

Keywords:

• pseudo-parabolic equations
• existence
• uniqueness
• variable exponents.

AMS Subject Classifications:

• 35K35
• 35K55
• 35K65

Acknowledgments

The authors would like to thank referees for his/her valuable suggestions and for providing the references S.Antontsev, S.Shmarev [27] and M. M. Porzio [28].

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.