### Electronic Research Archive

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

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

• 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.

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

### Related Papers:

• 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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