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Traveling wave fronts in reaction-diffusion systems with spatio-temporal delay and applications
This paper is concerned with monotone traveling wave solutions of
reaction-diffusion systems with spatio-temporal
delay. Our approach is to use a new monotone
iteration scheme based on a lower solution in the set of the profiles. The smoothness of upper and lower solutions is not
required in this paper. We will apply our results to
Nicholson's blowflies systems with non-monotone birth functions and show that the systems admit traveling wave solutions connecting two spatially
homogeneous equilibria and the wave shape is monotone. Due to the biological realism, the positivity of the
monotone traveling wave solutions can be directly obtained by the construction of suitable upper-lower
solutions.