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

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 in...

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Bibliographic Details
Published in:Electronic research archive 2021-12, Vol.29 (6), p.3833-3851
Main Authors: Cao, Yang, Zhao, Qiuting
Format: Article
Language:English
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Summary: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.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2021064