Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations

Yang Cao; Qiuting Zhao; Yang Cao; Qiuting Zhao

doi:10.3934/era.2021064

Electronic Research Archive

2021, Volume 29, Issue 6: 3833-3851. doi: 10.3934/era.2021064

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Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations

Yang Cao ^,,
Qiuting Zhao

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received: 01 January 2021 Revised: 01 July 2021 Published: 07 September 2021
Primary: 35K70, 35B40; Secondary: 35K35

In this paper, we consider the initial boundary value problem for a mixed pseudo-parabolic Kirchhoff equation. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions with initial energy $ J(u_0)\leq d $. When the initial energy $ J(u_0)>d $, we find another criterion for the vanishing solution and blow-up solution. Our interest also lies in the discussion of the exponential decay rate of the global solution and life span of the blow-up solution.
- Pseudo-parabolic,
- Kirchhoff equation,
- global existence,
- blow-up
Citation: Yang Cao, Qiuting Zhao. Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations[J]. Electronic Research Archive, 2021, 29(6): 3833-3851. doi: 10.3934/era.2021064

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Abstract

In this paper, we consider the initial boundary value problem for a mixed pseudo-parabolic Kirchhoff equation. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions with initial energy $ J(u_0)\leq d $. When the initial energy $ J(u_0)>d $, we find another criterion for the vanishing solution and blow-up solution. Our interest also lies in the discussion of the exponential decay rate of the global solution and life span of the blow-up solution.

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