Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 20, Number 4 (2016), 801-822.
Stability of Traveling Wave Fronts for Nonlocal Diffusion Equation with Delayed Nonlocal Response
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.
Taiwanese J. Math., Volume 20, Number 4 (2016), 801-822.
First available in Project Euclid: 1 July 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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