| Abstract: |
| In this talk, we are concerned with the stability of monostable traveling waves of scalar reaction-diffusion equations and systems with delay. Especially, it is more difficult to investigate the stability of critical waves of delayed systems without quasi-monotonicity for the facts that comparison principle does not hold for the scarcity of quasi-monotonicity in equations; the normally weighted energy method can not be applied to monostable traveling waves in the case of critical speed for their asymptotic behaviors at positive infinity and it is not easy to get the decay estimates of elementary solutions of ordinary functional differential equations because of the coupling of different unknown functions, and thus it is not suitable any longer by using the frequent methods and normal theory to solve the stability of traveling wave solutions for classical reaction-diffusion equations. Therefore, it brings a new challenge to develop and improve theory of traveling waves of reaction-diffusion equations with delay. |
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