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Traveling wave fronts in reaction-diffusion systems with spatio-temporal delay and applications. (English) Zbl 1206.35244
The authors develop a monotone iteration approach to prove the existence of monotone traveling wave solutions for reaction-diffusion equation $$u(t,x)'_t=Du(t,x)_{xx}''+f(u(t,x),(g_1*u)(t,x),\dots, (g_m*u)(t,x)). $$ As an application the Nicholson’s blowfliers equation with non-monotone birth functions and different kernels are considered. A main contribution of this paper is to get existence of monotone waves in non-monotone system.

35R10Partial functional-differential equations
35K57Reaction-diffusion equations
35Q92PDEs in connection with biology and other natural sciences
35C07Traveling wave solutions of PDE
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