| Abstract: |
| We mainly focus on the entire solutions of a nonlocal dispersal equation with asymmetric kernel function and different reaction terms, such as monostable, bistable and ignition nonlinearities. Compared with symmetric case, the asymmetry of the dispersal kernel function has a great influence on the profile of the traveling waves and the sign and size of the wave speeds, which further makes the types and properties of the entire solution more diverse. Accoding to different reaction terms, we established many different front-like entire solutions and investigated their qualitative features. Before this, we characterize the precise asymptotic behaviors of the traveling wave solutions at infinity since they play an important role in obtaining entire solutions. |
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