On a non-local equation arising in population dynamics
On a non-local equation arising in population dynamics
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DOI：
10.1017/s0308210504000721
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发表时间：
2007-01-01
影响因子：
1.3
通讯作者：
Dupaigne, Louis
中科院分区：
文献类型：
--
作者：
Coville, Jerome;Dupaigne, Louis
我们研究了描述突变体在给定种群中的空间扩散的Fisher方程的一维非局部变体，并将其推广到所谓的单稳定非线性。假设遗传性状的分散遵循由卷积算子建模的非局部扩散规律。我们证明了在经典（局部）问题中，存在超过临界值的任意速度的行波解，并刻画了这种解在无穷远处的渐近行为。我们的证明依赖于极大值原理的适当版本，解的定性性质和导致奇异极限的近似格式。
We study a one-dimensional non-local variant of Fisher's equation describing the spatial spread of a mutant in a given population, and its generalization to the so-called monostable nonlinearity. The dispersion of the genetic characters is assumed to follow a non-local diffusion law modelled by a convolution operator. We prove that, as in the classical (local) problem, there exist travelling-wave solutions of arbitrary speed beyond a critical value and also characterize the asymptotic behaviour of such solutions at infinity. Our proofs rely on an appropriate version of the maximum principle, qualitative properties of solutions and approximation schemes leading to singular limits.