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Generalized Fronts in Reaction-Diffusion Equations with Bistable Nonlinearity

Generalized Fronts in Reaction-Diffusion Equations with Bistable Nonlinearity
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摘要 In this paper, we first study the existence of transition fronts （generalized traveling fronts） for reaction-diffusion equations with the spatially heterogeneous bistable nonlinearity. By constructing sub-solution and super-solution we then show that transition fronts are globally exponentially stable for the solutions of the Cauchy problem. Furthermore, we prove that transition fronts are unique up to translation in time by using the monotonicity in time and the exponential decay of such transition fronts. In this paper, we first study the existence of transition fronts （generalized traveling fronts） for reaction-diffusion equations with the spatially heterogeneous bistable nonlinearity. By constructing sub-solution and super-solution we then show that transition fronts are globally exponentially stable for the solutions of the Cauchy problem. Furthermore, we prove that transition fronts are unique up to translation in time by using the monotonicity in time and the exponential decay of such transition fronts.
作者 Ya Qin SHU Wan Tong LI Nai Wei LIU
机构地区 School of Mathematics and Statistics School of Mathematics and Statistics School of Mathematics and Informational Science
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第8期1633-1646,共14页 数学学报（英文版）
基金 Supported by NSF of China(Grant No.11031003) NSF of Shandong Province of China(Grant No.ZR2010AQ006)
关键词 Reaction-diffusion equation transition fronts UNIQUENESS bistable nonlinearity stability Reaction-diffusion equation, transition fronts, uniqueness, bistable nonlinearity, stability
分类号 O175 [理学—基础数学]
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参考文献33

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Acta Mathematica Sinica,English Series
2012年 第8期

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