Spreading speeds and traveling waves for abstract monostable evolution systems |
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| Authors: | Xing Liang Xiao-Qiang Zhao |
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| Institution: | a Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
b Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada |
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| Abstract: | This paper is devoted to the development of the theory of spreading speeds and traveling waves for abstract monostable evolution systems with spatial structure. Under appropriate assumptions, we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative directions. Then we use this theory to study the spatial dynamics of a parabolic equation in a periodic cylinder with the Dirichlet boundary condition, a reaction-diffusion model with a quiescent stage, a porous medium equation in a tube, and a lattice system in a periodic habitat. |
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| Keywords: | Monotone semiflows Spreading speeds Traveling waves Evolution systems Periodic habitat |
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