Remark on Stability of Traveling Waves for Nonlocal Fisher-Kpp Equations
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@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^{-ν_τt} for some constant ν_τ=ν(τ)> 0, where
τ≥ 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 τ 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}
}
TY - JOUR
T1 - Remark on Stability of Traveling Waves for Nonlocal Fisher-Kpp Equations
AU - MING MEI AND YONG WANG
JO - International Journal of Numerical Analysis Modeling Series B
VL - 4
SP - 379
EP - 401
PY - 2011
DA - 2011/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/319.html
KW - Nonlocal reaction-diffusion equations
KW - time delays
KW - traveling waves
KW - global stability
KW - the Fisher-KPP equation
KW - L^1-weighted energy
KW - Green functions
AB - 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^{-ν_τt} for some constant ν_τ=ν(τ)> 0, where
τ≥ 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 τ 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.
MING MEI AND YONG WANG. (1970). Remark on Stability of Traveling Waves for Nonlocal Fisher-Kpp Equations.
International Journal of Numerical Analysis Modeling Series B. 2 (4).
379-401.
doi:
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