Entire solutions of reaction-advection-diffusion equations with bistable nonlinearity in cylinders |
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Authors: | Nai-Wei Liu Zhi-Cheng Wang |
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Affiliation: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China |
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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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Keywords: | 35K57 35B05 35B40 34K30 |
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