TY - JOUR
T1 - Effect of noise on front propagation in reaction-diffusion equations of KPP type
AU - Mueller, Carl
AU - Mytnik, Leonid
AU - Quastel, Jeremy
N1 - Funding Information:
L. Mytnik was supported in part by the Israel Science Foundation (grant No. 1162/06).
Funding Information:
J. Quastel was supported by NSERC, Canada.
Funding Information:
C. Mueller was supported by an NSF grant.
PY - 2011/5
Y1 - 2011/5
N2 - We consider reaction-diffusion equations of KPP type in one spatial dimension, perturbed by a Fisher-Wright white noise, under the assumption of uniqueness in distribution. Examples include the randomly perturbed Fisher-KPP equations, and, where Ẇ = Ẇ(t,x) is a space-time white noise. We prove the Brunet-Derrida conjecture that the speed of traveling fronts for small ε is.
AB - We consider reaction-diffusion equations of KPP type in one spatial dimension, perturbed by a Fisher-Wright white noise, under the assumption of uniqueness in distribution. Examples include the randomly perturbed Fisher-KPP equations, and, where Ẇ = Ẇ(t,x) is a space-time white noise. We prove the Brunet-Derrida conjecture that the speed of traveling fronts for small ε is.
KW - Random traveling fronts
KW - Reaction-diffusion equation
KW - Stochastic partial differential equations
KW - White noise
UR - http://www.scopus.com/inward/record.url?scp=79955048916&partnerID=8YFLogxK
U2 - 10.1007/s00222-010-0292-5
DO - 10.1007/s00222-010-0292-5
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AN - SCOPUS:79955048916
SN - 0020-9910
VL - 184
SP - 405
EP - 453
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -