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This short note is to fix the gap for the proof of Lemma 3.8 in our previous paper In our previous paper [2], in order to get the algebraic stability for the critical traveling wavefronts, one of key steps is to build up the decay estimate (see Lemma 3.8 in [2]) ¯ v(t) L ∞ w 1 (R) ≤ C(1 + t) − 1 2 , (0.1) where w 1 (ξ) = e −λ * (ξ−x0) is the weight function(More)
This paper considers the nonlinear stability of travelling wavefronts of a time-delayed diffusive Nicholson blowflies equation. We prove that, under a weighted L 2 norm, if a solution is sufficiently close to a travelling wave front initially, it converges exponentially to the wavefront as t → ∞. The rate of convergence is also estimated.
This paper is concerned with a class of nonlocal Fisher-KPP type reaction-diffusion equations in n-dimensional space with time-delay. It is proved that, all noncritical planar wave-fronts are exponentially stable in the form of t − n 2 e −ντ t for some constant ντ = ν(τ) > 0, where τ ≥ 0 is the time-delay, while the critical planar wavefronts are(More)
In this paper we present a physically relevant hydrodynamic model for a bipolar semiconductor device considering Ohmic conductor boundary conditions and a non-flat doping profile. For such an Euler-Poisson system, we prove, by means of a technical energy method, that the solutions are unique, exist globally and asymptotically converge to the corresponding(More)
The paper is devoted to the study of a time-delayed reaction- diffusion equation of age-structured single species population. Linear stability for this model was first presented by Gourley [4], when the time delay is small. Here, we extend the previous result to the nonlinear stability by using the technical weighted-energy method, when the initial(More)