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Salako, Wenxian Shen","submitted_at":"2018-06-09T17:22:09Z","abstract_excerpt":"In the current series of two papers, we study the long time behavior of the following random Fisher-KPP equation $$ u_t =u_{xx}+a(\\theta_t\\omega)u(1-u),\\quad x\\in\\R, \\eqno(1) $$ where $\\omega\\in\\Omega$, $(\\Omega, \\mathcal{F},\\mathbb{P})$ is a given probability space, $\\theta_t$ is an ergodic metric dynamical system on $\\Omega$, and $a(\\omega)>0$ for every $\\omega\\in\\Omega$. We also study the long time behavior of the following nonautonomous Fisher-KPP equation, $$ u_t=u_{xx}+a_0(t)u(1-u),\\quad x\\in\\R, \\eqno(2) $$ where $a_0(t)$ is a positive locally H\\\"older continuous function. 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