Spatial decay and stability of traveling fronts for degenerate Fisher type equations in cylinder

He, Junfeng; Wu, Yaqi

doi:10.1016/j.jde.2018.06.031

Journal of Differential Equations

2018

DOI: 10.1016/j.jde.2018.06.031

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Spatial decay and stability of traveling fronts for degenerate Fisher type equations in cylinder

Junfeng He

Yaqi Wu

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Cited by 9 publications

(2 citation statements)

References 28 publications

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“…Therefore (9) gives an upper estimate for the solution w(t, x) to the Cauchy problem (8). Similarly, the lower estimate for w(t, x) can be given by the Cauchy problem…”

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confidence: 93%

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Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations

2021

era

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<p style='text-indent:20px;'>In this paper, multidimensional stability of pyramidal traveling fronts are studied to the reaction-diffusion equations with degenerate Fisher-KPP monostable and combustion nonlinearities. By constructing supersolutions and subsolutions coupled with the comparison principle, we firstly prove that under any initial perturbation (possibly large) decaying at space infinity, the three-dimensional pyramidal traveling fronts are asymptotically stable in weighted <inline-formula><tex-math id="M1">\begin{document}$ L^{\infty} $\end{document}</tex-math></inline-formula> spaces on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^{n}\; (n\geq4) $\end{document}</tex-math></inline-formula>. Secondly, we show that under general bounded perturbations (even very small), the pyramidal traveling fronts are not asymptotically stable by constructing a solution which oscillates permanently between two three-dimensional pyramidal traveling fronts on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^{4} $\end{document}</tex-math></inline-formula>.</p>

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“…Therefore (9) gives an upper estimate for the solution w(t, x) to the Cauchy problem (8). Similarly, the lower estimate for w(t, x) can be given by the Cauchy problem…”

mentioning

confidence: 93%

“…(1) with Fisher-KPP nonlinearity, non-KPP monostable and combustion nonlinearity, respectively. He and Wu [8] using spectral method studied the stability of traveling front for degenerate Fisher type equations.…”

mentioning

confidence: 99%

Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations

2021

era

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The asymptotic stability of diverging traveling waves for reaction–advection–diffusion equations in cylinders

Jia,

Wang,

Guo

2024

Z. Angew. Math. Phys.

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The Role of Delay and Degeneracy on Propagation Dynamics in Diffusion Equations

Lin

2021

J Dyn Diff Equat

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Spatial decay and stability of traveling fronts for degenerate Fisher type equations in cylinder

Cited by 9 publications

References 28 publications

Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations

Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations

The asymptotic stability of diverging traveling waves for reaction–advection–diffusion equations in cylinders

The Role of Delay and Degeneracy on Propagation Dynamics in Diffusion Equations

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