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- W3103269364 abstract "We study the wavefront solutionsof the scalar reaction-diffusion equations $u_{t}(t,x) = Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone reaction term $g: mathbb{R}_{+} → mathbb{R}_+$ and $h >0$. We are mostly interestedin the situation when the graph of $g$ is not dominated by its tangent line at zero, i.e. when the condition $g(x) leq g'(0)x,$ $x geq 0$, is not satisfied. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with $h=0$). One of our main goals here is to establish a similar result for $h>0$. To this end, we describe the asymptotics of all wavefronts (including critical and non-critical fronts) at $-infty$. We also prove the uniqueness of wavefronts (up to a translation). In addition, a new uniqueness result for a class of nonlocal lattice equations is presented." @default.
- W3103269364 created "2020-11-23" @default.
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- W3103269364 date "2013-01-01" @default.
- W3103269364 modified "2023-10-17" @default.
- W3103269364 title "Pushed traveling fronts in monostable equations with monotone delayed reaction" @default.
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- W3103269364 doi "https://doi.org/10.3934/dcds.2013.33.2169" @default.
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