Pushed traveling fronts in monostable equations with monotone delayed reaction

Details Pushed traveling fronts in monostable equations with monotone delayed reaction Pushed traveling fronts in monostable equations with monotone delayed reaction

2011-11-22

arxiv.org/abs/1111.5161v1

Mathematics

Analysis of PDEs

17 pages, submitted

Scientific paper

We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested in 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 $h>0$. We prove the existence of the minimal speed of propagation, the uniqueness of wavefronts (up to a translation) and describe their asymptotics at $-\infty$. We also present a new uniqueness result for a class of nonlocal lattice equations.

Affiliated with

Also associated with

No associations

Rating

Pushed traveling fronts in monostable equations with monotone delayed reaction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Pushed traveling fronts in monostable equations with monotone delayed reaction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pushed traveling fronts in monostable equations with monotone delayed reaction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-553087