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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 , 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 ) ¯ 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.
All papers of the present volume were peer reviewed by no less that two independent reviewers. Acceptance was granted when both reviewers' recommendations were positive.
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 , 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)