Electron. J. Differential Equations, Vol. 2018 (2018), No. 116, pp. 1-19.

Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity

Yang Cao, Conghui Liu

Abstract:
We consider the initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. Constructing a family of potential wells and using the logarithmic Sobolev inequality, we establish the existence of global weak solutions. we consider two cases: global boundedness and blowing-up at infinity. Moreover, we discuss the asymptotic behavior of solutions and give some decay estimates and growth estimates.

Submitted December 26, 2017. Published May 14, 2018.
Math Subject Classifications: 35K58, 35K35, 35B40.
Key Words: Pseudo-parabolic; p-Laplacian; logarithmic nonlinearity; long time behavior.

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Yang Cao
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: mathcy@dlut.edu.cn
Conghui Liu
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: conghuil@sina.com

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