Effect of noise on front propagation in reaction-diffusion equations of KPP type

Carl Mueller; Leonid Mytnik; Jeremy Quastel

doi:10.1007/s00222-010-0292-5

Effect of noise on front propagation in reaction-diffusion equations of KPP type

Carl Mueller, Leonid Mytnik, Jeremy Quastel

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	405-453
Number of pages	49
Journal	Inventiones Mathematicae
Volume	184
Issue number	2
DOIs	https://doi.org/10.1007/s00222-010-0292-5
State	Published - May 2011

Keywords

Random traveling fronts
Reaction-diffusion equation
Stochastic partial differential equations
White noise

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-010-0292-5

Cite this

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title = "Effect of noise on front propagation in reaction-diffusion equations of KPP type",

abstract = "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.",

keywords = "Random traveling fronts, Reaction-diffusion equation, Stochastic partial differential equations, White noise",

author = "Carl Mueller and Leonid Mytnik and Jeremy Quastel",

note = "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.",

year = "2011",

month = may,

doi = "10.1007/s00222-010-0292-5",

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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

M3 - مقالة

SN - 0020-9910

VL - 184

SP - 405

EP - 453

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 2

ER -

Effect of noise on front propagation in reaction-diffusion equations of KPP type

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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