Taiwanese Journal of Mathematics

Stability of Traveling Wave Fronts for Nonlocal Diffusion Equation with Delayed Nonlocal Response

Hongmei Cheng and Rong Yuan

Full-text: Open access

Abstract

In this paper, we consider with the stability of traveling wave fronts for the nonlocal diffusion equation with delay and global response. We first establish the existence and comparison theorem of solutions for the nonlocal reaction-diffusion equation by appealing to the theory of abstract functional differential equation. Then we further show that the traveling wave fronts are asymptotical stability with phase shift. Our main technique is the super and subsolution method coupled with the comparison principle and squeezing method.

Article information

Source
Taiwanese J. Math., Volume 20, Number 4 (2016), 801-822.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874492

Digital Object Identifier
doi:10.11650/tjm.20.2016.6284

Mathematical Reviews number (MathSciNet)
MR3535675

Zentralblatt MATH identifier
1357.35075

Subjects
Primary: 35R10: Partial functional-differential equations 35B40: Asymptotic behavior of solutions 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 58D25: Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]

Keywords
nonlocal diffusion asymptotic stability traveling wave fronts super and subsolution comparison principle squeezing method delayed nonlocal response

Citation

Cheng, Hongmei; Yuan, Rong. Stability of Traveling Wave Fronts for Nonlocal Diffusion Equation with Delayed Nonlocal Response. Taiwanese J. Math. 20 (2016), no. 4, 801--822. doi:10.11650/tjm.20.2016.6284. https://projecteuclid.org/euclid.twjm/1498874492


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