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Stochastic traveling wave solution to stochastic generalized KPP equation

  • Zhehao HuangEmail author
  • Zhengrong Liu
Article
  • 324 Downloads

Abstract

In this paper, we consider a stochastic generalized KPP equation driven by a white noise term. Denote u the solution to the equation with Heaviside initial condition \({u_{0}(x) = \chi_{(-\infty,0]}(x)}\). Choosing a suitable marker of wavefront R(t), we prove that \({u(t,\cdot+R(t))}\) is a stationary process and \({\lim_{t\rightarrow\infty}R(t)/t}\) exists almost surely, which verify the existence of stochastic traveling wave solution to the equation.

Mathematics Subject Classification (2010)

Primary 99Z99 Secondary 00A00 

Keywords

Wavefront Stationary process Stochastic traveling wave solution Stochastic generalized KPP equation 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsSouth China University of TechnologyGuangzhouPeople’s Republic of China

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