NONEXISTENCE OF COEXISTING STEADY-STATE SOLUTIONS FOR A REACTION-DIFFUSION COMPETING SYSTEM WITH FRACTIONAL TYPE CROSS-DIFFUSION

Ningning Zhu; Fanwei Meng

doi:10.11948/20250005

2025 Volume 15 Issue 6

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Ningning Zhu, Fanwei Meng. NONEXISTENCE OF COEXISTING STEADY-STATE SOLUTIONS FOR A REACTION-DIFFUSION COMPETING SYSTEM WITH FRACTIONAL TYPE CROSS-DIFFUSION[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3403-3413. doi: 10.11948/20250005

Citation:

Ningning Zhu, Fanwei Meng. NONEXISTENCE OF COEXISTING STEADY-STATE SOLUTIONS FOR A REACTION-DIFFUSION COMPETING SYSTEM WITH FRACTIONAL TYPE CROSS-DIFFUSION[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3403-3413. doi: 10.11948/20250005

NONEXISTENCE OF COEXISTING STEADY-STATE SOLUTIONS FOR A REACTION-DIFFUSION COMPETING SYSTEM WITH FRACTIONAL TYPE CROSS-DIFFUSION

Ningning Zhu^1,,
Fanwei Meng^1, ,

1.
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China

Author Bio: Email: znn199192@163.com(N. Zhu)
Corresponding author: Email: fwmeng@qfnu.edu.cn(F. Meng)
Fund Project: The authors were supported by Natural Science Foundation of Shandong Province (No. ZR2021QA103)

Abstract

Abstract

We discuss a system of two competing species with fractional type cross-diffusion. The basic idea is to make a link among the extreme values of steady-state solutions according to the maximum principle. Then by introducing a proper discriminant function, which is monotonically decreasing, we establish sufficient conditions such that the system has no coexisting steady-state solutions.
- Fractional type cross-diffusion /
- steady-state /
- coexisting solution
MSC: 35J60, 35A01

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References

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