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• W2093778075 abstract "This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case of a reaction-diffusion equation in a periodic medium with ignition-type nonlinearity, the heterogeneity being on the nonlinearity, the operator, and the domain. Contrary to previous works, we study the asymptotic spreading properties of the solutions of the Cauchy problem with general initial conditions which satisfy very mild assumptions at infinity. We introduce several concepts generalizing the notion of spreading speed, and we give a complete characterization of it when the initial condition is asymptotically oscillatory at infinity. Furthermore we construct, even in the homogeneous one-dimensional case, a class of initial conditions for which highly nontrivial dynamics can be exhibited." @default.
• W2093778075 created "2016-06-24" @default.
• W2093778075 creator A5045752660 @default.
• W2093778075 creator A5052288200 @default.
• W2093778075 date "2010-01-01" @default.
• W2093778075 modified "2023-09-27" @default.
• W2093778075 title "Spreading Speeds for Some Reaction-Diffusion Equations with General Initial Conditions" @default.
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• W2093778075 doi "https://doi.org/10.1137/090759409" @default.
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