Generalized Fronts in Reaction-Diffusion Equations with Bistable Nonlinearity  

作　　者：Ya Qin SHU Wan Tong LI Nai Wei LIU 

机构地区：[1]School of Mathematics and Statistics,Chongqing University of Technology [2]School of Mathematics and Statistics,Lanzhou University [3]School of Mathematics and Informational Science,Yantai University

出　　处：《Acta Mathematica Sinica,English Series》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)

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.

关 键 词：Reaction-diffusion equation transition fronts UNIQUENESS bistable nonlinearity stability 

分 类 号：O175[理学—数学]