Entire solutions in reaction-advection-diffusion equations in cylinders

By Wanwan Li, Nai‐Wei Liu, Zhi-Cheng Wang. 2008

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This paper is concerned with the existence of entire solutions of a reaction-advection-diffusion equation with monostable and ignition temperature nonlinearities in infinite-cylinders. Here the entire solutions are defined in the whole infinite cylinder and for all time t∈R. A comparison argument is used to prove the existence of entire solutions which behave as two traveling wave fronts coming from both directions. The main techniques are to characterize the asymptotic behavior of the solutions as t→−∞ in term of appropriate subsolutions and supersolutions. In order to illustrate our main results, a passive-reaction-diffusion equation model arising from propagation of fronts is considered. This is probably the first time the existence of entire solutions of reaction-diffusion equations in infinite-cylinders has been studied.

Subfields: Applied Mathematics, Control and Systems Engineering, Public Health, Environmental and Occupational Health

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