The Bramson logarithmic delay in the cane toads equations
The Bramson logarithmic delay in the cane toads equations
复制标题
甘蔗蟾蜍方程中的布拉姆森对数延迟
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
L. Ryzhik
中科院分区：
文献类型：
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作者：
E. Bouin;Christopher Henderson;L. Ryzhik
我们研究了一个非局部的反应扩散突变方程建模的甘蔗蟾蜍种群的扩散由一个表型性状负责的空间扩散率。当特征空间有界时，甘蔗蟾蜍方程存在行波解[7]。在这里，我们证明了Bramson型的扩展结果：与本地化的初始数据和行波的位置之间的滞后增长为（3/（2 $\lambda $ *））log t的解决方案。这一结果依赖于一个目前的Harnack不等式，它允许甘蔗蟾蜍方程的解决方案进行比较的费舍尔-KPP型方程，是本地的性状变量。
We study a nonlocal reaction-diffusion-mutation equation modeling the spreading of a cane toads population structured by a phenotypical trait responsible for the spatial diffusion rate. When the trait space is bounded, the cane toads equation admits traveling wave solutions [7]. Here, we prove a Bramson type spreading result: the lag between the position of solutions with localized initial data and that of the traveling waves grows as (3/(2$\lambda$ *)) log t. This result relies on a present-time Harnack inequality which allows to compare solutions of the cane toads equation to those of a Fisher-KPP type equation that is local in the trait variable.