期刊
NONLINEARITY
卷 23, 期 3, 页码 675-686出版社
IOP PUBLISHING LTD
DOI: 10.1088/0951-7715/23/3/014
关键词
-
资金
- French 'Agence Nationale de la Recherche'
This paper is devoted to the analysis of some uniqueness properties of a classical reaction-diffusion equation of the Fisher-KPP type, coming from population dynamics in heterogeneous environments. We work in a one-dimensional interval (a, b) and we assume a nonlinear term of the form u (mu(x) - gamma u) where mu belongs to a fixed subset of C-0([a, b]). We prove that the knowledge of u at t = 0 and of u, u(x) at a single point x(0) and for small times t is an element of (0, epsilon) is sufficient to completely determine the couple (u(t, x), mu(x)) provided. is known. Additionally, if u(xx)(t, x(0)) is also measured for t is an element of (0, epsilon), the triplet (u(t, x), mu(x), gamma) is also completely determined. Those analytical results are completed with numerical simulations which show that, in practice, measurements of u and u(x) at a single point x(0) (and for t is an element of (0, epsilon)) are sufficient to obtain a good approximation of the coefficient mu(x). These numerical simulations also show that the measurement of the derivative u(x) is essential in order to accurately determine mu(x).
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据