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- W2762298936 abstract "We consider the reaction-diffusion equation begin{equation*} u_t=u_{xx}+muleft(int_Omega M(y,z)u(t,x,z)dz-uright) + uleft(a(y)-int_Omega K(y,z) u(t,x,z)dzright) , end{equation*} where $ u=u(t,x,y) $ stands for the density of a theoretical population with a spatial ($xinmathbb R$) and phenotypic ($yinOmegasubset mathbb R^n$) structure, $ M(y,z) $ is a mutation kernel acting on the phenotypic space, $ a(y) $ is a fitness function and $ K(y,z) $ is a competition kernel. Using a vanishing viscosity method, we construct measure-valued traveling waves for this equation, and present particular cases where singular traveling waves do exist. We determine that the speed of the constructed traveling waves is the expected spreading speed $ c^*:=2sqrt{-lambda_1} $, where $ lambda_1 $ is the principal eigenvalue of the linearized equation. As far as we know, this is the first construction of a measure-valued traveling wave for a reaction-diffusion equation." @default.
- W2762298936 created "2017-10-20" @default.
- W2762298936 creator A5065557169 @default.
- W2762298936 date "2018-11-13" @default.
- W2762298936 modified "2023-09-23" @default.
- W2762298936 title "Singular measure traveling waves in an epidemiological model with continuous phenotypes" @default.
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- W2762298936 doi "https://doi.org/10.1090/tran/7700" @default.
- W2762298936 hasPublicationYear "2018" @default.
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