Decay estimate and blow-up for fractional Kirchhoff wave equations involving a logarithmic source

Aihui Sun; Hui Xu; Aihui Sun; Hui Xu

doi:10.3934/math.2025631

AIMS Mathematics

2025, Volume 10, Issue 6: 14032-14054. doi: 10.3934/math.2025631

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Decay estimate and blow-up for fractional Kirchhoff wave equations involving a logarithmic source

Aihui Sun ^{1
,
,},
Hui Xu ²

1.
College of Mathematics and Computer, Jilin Normal University, Siping 136000, China
2.
College of Mathematics and Statistics, Baicheng Normal University, Baicheng 137000, China

Received: 31 March 2025 Revised: 24 April 2025 Accepted: 04 June 2025 Published: 18 June 2025
MSC : 35A01, 35B40, 35B44, 35R11

This paper was dedicated to researching a class of fractional Kirchhoff wave models involving a logarithmic source and strong damping term. We have proven the local existence and uniqueness of weak solutions through combining contraction mapping theory with Faedo-Galerkin's method. Based on the framework of a potential well and under suitable conditions, an exponential decay estimate of global weak solutions was established. Finally, the result of the finite time blow-up was obtained.
- decay estimate,
- blow-up,
- fractional Laplacian,
- Kirchhoff wave equations,
- logarithmic source
Citation: Aihui Sun, Hui Xu. Decay estimate and blow-up for fractional Kirchhoff wave equations involving a logarithmic source[J]. AIMS Mathematics, 2025, 10(6): 14032-14054. doi: 10.3934/math.2025631

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Abstract

This paper was dedicated to researching a class of fractional Kirchhoff wave models involving a logarithmic source and strong damping term. We have proven the local existence and uniqueness of weak solutions through combining contraction mapping theory with Faedo-Galerkin's method. Based on the framework of a potential well and under suitable conditions, an exponential decay estimate of global weak solutions was established. Finally, the result of the finite time blow-up was obtained.

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