BEHAVIOR OF SOLUTIONS TO A COUPLED KIRCHHOFF-TYPE PARABOLIC SYSTEM WITH SINGULAR POTENTIAL AND LOGARITHMIC NONLINEARITY

Ruixi Li; Mengrui Yang; Tingfu Feng; Huan Meng

doi:10.11948/20250315

2026 Volume 16 Issue 4

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Ruixi Li, Mengrui Yang, Tingfu Feng, Huan Meng. BEHAVIOR OF SOLUTIONS TO A COUPLED KIRCHHOFF-TYPE PARABOLIC SYSTEM WITH SINGULAR POTENTIAL AND LOGARITHMIC NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1978-2018. doi: 10.11948/20250315

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Ruixi Li, Mengrui Yang, Tingfu Feng, Huan Meng. BEHAVIOR OF SOLUTIONS TO A COUPLED KIRCHHOFF-TYPE PARABOLIC SYSTEM WITH SINGULAR POTENTIAL AND LOGARITHMIC NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1978-2018. doi: 10.11948/20250315

BEHAVIOR OF SOLUTIONS TO A COUPLED KIRCHHOFF-TYPE PARABOLIC SYSTEM WITH SINGULAR POTENTIAL AND LOGARITHMIC NONLINEARITY

1.
Department of Mathematics, Kunming University, Kunming, Yunnan, China

Author Bio: Email: ruixili0321@163.com(R. Li); Email: mengruiyang2023@163.com(M. Yang); Email: huanmeng0415@163.com(H. Meng)
Corresponding author: Email: fengtingfu@kmu.edu.cn(T. Feng)
Fund Project: This work is sponsored by the National Natural Science Foundation of China (Grant No. 12261053), the project Science and Technology Project of Yunnan Province, Key Technology Projects in Yunnan Province (No. 202302AF080003), the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities Association (Grant Nos. 202401BA070001-110, 202301BA070001-002, 202101BA070001-132), and the Scientific Research Fund of Education Department of Yunnan Province (Grant Nos. 2024Y775, 2024Y776, 2025Y1076, 2024J0775)

Abstract

Abstract

In this paper, we apply the modified potential well method and the variational method to study the long-time behaviors of solutions to a coupled Kirchhoff-type parabolic system with singular potential and logarithmic nonlinearity. By classifying the initial energy (J(u₀, v₀) < d, = d, > d), we obtain global existence and finite-time blow-up of solutions. Noting that the value of the potential well depth d is very small such that it is difficult to calculate precisely, by the concavity method, we also discuss finite time blow-up of solutions independent of d. Furthermore, we derive new threshold criteria for extinction and non-extinction phenomena of solutions, and obtain the threshold time for the extinction phenomenon under some appropriate conditions.
- Coupled Kirchhoff-type parabolic system /
- global existence /
- blow up /
- extinction /
- non-extinct
MSC: 35K52, 35A01, 35B44

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References

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