@Article{IJNAMB-2-379,
author = {MING MEI AND YONG WANG},
title = {Remark on Stability of Traveling Waves for Nonlocal Fisher-Kpp Equations},
journal = {International Journal of Numerical Analysis Modeling Series B},
year = {2011},
volume = {2},
number = {4},
pages = {379--401},
abstract = {This paper is concerned with a class of nonlocal Fisher-KPP type reaction-diffusion equations in n-dimensional space with time-delay. It is proved that, all noncritical planar wavefronts
are exponentially stable in the form of t^{-\frac{n}{2}}e^{-&#957_&#964t} for some constant &#957_&#964=&#957(&#964)&#62 0, where
&#964&#8805 0 is the time-delay, while the critical planar wavefronts are algebraically stable in the form of
t^{-\frac{n}{2}}. These convergent rates are optimal in the sense with L^1-initial perturbation. The adopted
approach is the weighted energy method combining Fourier transform. It is also realized that,
the effect of time-delay essentially causes the decay rate of the solution slowly down. These results
significantly generalize and develop the existing study [37] for 1-D time-delayed Fisher-KPP
type reaction-diffusion equations. When the time-delay &#964 vanishes, we automatically obtain the
exponential stability for the noncritical planar traveling waves and the algebraic stability for the
critical planar traveling waves to the regular Fisher-KPP equations.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnamb/319.html}
}