| Abstract: |
| In this talk, the stability of monostable traveling waves for a class of asymmetric diffusion system with nonlocal effects and delay is considered, where the system can be quasi-monotone or non-quasimonotone and the kernel functions in diffusion terms and nonlocal reactions can both be asymmetric. Firstly, the global stability of monostable wavefronts for the asymmetric nonlocal diffusion system is established by the Fourier transform and the anti-weighted energy method, and a new technique is developed to control the real part of the Fourier transform of the asymmetric kernels by a bounded function, which is different from the case of symmetric kernels. Secondly, if the system can be non-quasimonotone, the global stability of monostable waves with the decay rate of the form an exponential function multiplying by an algebraic function is also obtained. Moreover, some concrete examples and numerical stimulations are included to confirm the theoretical conclusions. |
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