This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes m...This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave speeds and the symmetry of the corresponding nonincreasing and nondecreasing traveling waves.We divide the bistable case into two monostable cases by restricting the range of the variable, and obtain some merging-front entire solutions which behave as the coupling of monostable and bistable waves. Before this, we characterize the classification of the wave speeds so that the entire solutions can be constructed more clearly. Especially, we investigate the influence of the asymmetry of the kernel on the minimal and maximal wave speeds.展开更多
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 a...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.展开更多
基金partially supported by FRFCU(300102128108)the NSF of China(Grant No.11801038)+2 种基金partially supported by the NSF of China(Grant Nos.11671180 and 11731005)partially supported by the NSF of China(Grant No.11371179)partially supported by the NSF of China(Grant No.11201359)
文摘This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave speeds and the symmetry of the corresponding nonincreasing and nondecreasing traveling waves.We divide the bistable case into two monostable cases by restricting the range of the variable, and obtain some merging-front entire solutions which behave as the coupling of monostable and bistable waves. Before this, we characterize the classification of the wave speeds so that the entire solutions can be constructed more clearly. Especially, we investigate the influence of the asymmetry of the kernel on the minimal and maximal wave speeds.
基金Supported by NSF of China(Grant No.11031003)NSF of Shandong Province of China(Grant No.ZR2010AQ006)
文摘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.
