Abstract
This paper deals with entire solutions and the interaction of traveling wave fronts of bistable reaction–advection–diffusion equation with infinite cylinders. Assume that the equation admits three equilibria: two stable equilibria 0 and 1, and an unstable equilibrium θ. It is well known that there are different wave fronts connecting any two of those three equilibria. By considering a combination of any two of those different traveling wave fronts and constructing appropriate subsolutions and supersolutions, we establish three different types of entire solutions. Finally, we analyze a model for shear flows in cylinders to illustrate our main results.
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