Initial boundary value problem of pseudo‐parabolic Kirchhoff equations with logarithmic nonlinearity

In this paper, we consider the initial boundary value problem for a pseudo‐parabolic Kirchhoff equation with logarithmic nonlinearity. Using the potential well method, we obtain a threshold result of global existence and finite‐time blow‐up for the weak solutions with initial energy J(u0)≤d$$ J\left...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-01, Vol.47 (2), p.799-816
Main Authors: Zhao, Qiuting, Cao, Yang
Format: Article
Language:English
Subjects:
blow‐up
Boundary value problems
Decay rate
global existence
logarithmic nonlinearity
Logarithms
Nonlinearity
pseudo‐parabolic Kirchhoff equation
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Summary:In this paper, we consider the initial boundary value problem for a pseudo‐parabolic Kirchhoff equation with logarithmic nonlinearity. Using the potential well method, we obtain a threshold result of global existence and finite‐time blow‐up for the weak solutions with initial energy J(u0)≤d$$ J\left({u}_0\right)\le d $$. When the initial energy J(u0)>d$$ J\left({u}_0\right)>d $$, we find another criterion for the vanishing solution and blow‐up solution. We also establish the decay rate of the global solution and estimate the life span of the blow‐up solution. Meanwhile, we study the existence of the ground state solution to the corresponding stationary problem.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9684