Non-local dispersal and bistability

被引:37
|
作者
Hutson, V. [1 ]
Grinfeld, M.
机构
[1] Univ Sheffield, Dept Appl Math, Sheffield S3 7RH, S Yorkshire, England
[2] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark, Scotland
关键词
D O I
10.1017/S0956792506006462
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The scalar initial value problem u(1), = pDu + f(u), is a model for dispersal. Here a represents the density at point x of a compact spatial region Omega epsilon R" and time t, and u(.) is a function of t with values in some function space B. D is a bounded linear operator and f (u) is a bistable nonlinearity for the associated ODE u(1) = f (u). Problems of this type arise in mathematical ecology and materials science where the simple diffusion model with D = Delta is not sufficiently general. The study of the dynamics of the equation presents a difficult problem which crucially differs from the diffusion case in that the semiflow generated is not compactifying. We study the asymptotic behaviour of solutions and ask under what conditions each positive semi-orbit converges to an equilibrium (as in the case D = Delta). We develop a technique for proving that indeed convergence does hold for small p and show by constructing a counter-example that this result does not hold in general for all p.
引用
收藏
页码:221 / 232
页数:12
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