Mathematical Sciences: Solutions for Functional DifferentialEquations
数学科学:泛函微分方程的解
基本信息
- 批准号:9401823
- 负责人:
- 金额:$ 7.5万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:1994
- 资助国家:美国
- 起止时间:1994-07-15 至 1998-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
9401823 Nussbaum Many natural phenomena, for example, in biology, seem best described by nonlinear "functional differential equations" or "FDE's". Roughly speaking, FDE's are equations in which an unknown function of time t, x(t), appears and x'(t), the instantaneous rate of change of x(t) with time, depends in a specified way not only on x(t) but also on the past history of the function x. For example,in some models the rate of increase of a population of a class of mature red blood cells at time t may well depend on population levels of those same mature cells six to ten days earlier. A rigorous mathematical theory of of nonlinear FDE's poses serious challenges and various equations of interest in applications have been neglected. We propose to study some classes of examples which were, until quite recently, considered intractable, but for which it now seems possible to obtain a wide variety of surprisingly detailed theorems. The starting point of this proposal is the study of the equation (*), ax'(t) = f(x(t),x(t-r)), r = r(x(t)), where f and r are given functions and a0. Equation (*) and generalizations of equation (*) arise in a variety of applications. In joint work with John Mallet-Paret, the author has shown that, under natural assumptions on f and r and for all sufficiently small a, equation (*) has nonconstant periodic solutions. These periodic solutions often seem to have strong global stability properties. Furthermore, in many cases it has proved possible to determine the limiting profile of shape of such periodic solutions as a approaches zero. In this proposal we consider many questions about equation (*), and we discuss possible extensions of results for (*) to much more general classes of equations.
9401823 Nussbaum许多自然现象,例如生物学中的许多自然现象,似乎都可以用非线性“泛函微分方程”或“泛函微分方程”来描述。粗略地说,FDE是这样的方程,其中出现未知的时间t的函数x(T),以及x(T)随时间的瞬时变化率x‘(T)不仅取决于x(T),而且取决于函数x的过去历史。例如,在某些模型中,某类成熟红细胞在时间t的增长率很可能取决于6至10天前那些相同的成熟细胞的种群水平。严格的非线性偏微分方程组的数学理论提出了严重的挑战,各种有趣的方程在应用中被忽视了。我们建议研究一些直到最近还被认为是难以解决的例子,但现在似乎有可能获得各种各样令人惊讶的详细定理。这个建议的出发点是研究方程(*),ax‘(T)=f(x(T),x(t-r)),r=r(x(T)),其中f和r是给定的函数和a0。方程式(*)和方程式(*)的推广在各种应用中出现。在与John Mallet-Paret的合作中,作者证明了,在关于f和r的自然假设下,对所有足够小的a,方程(*)有非常数周期解。这些周期解往往具有很强的全局稳定性。此外,在许多情况下,已经证明可以确定当a趋近于零时这种周期解的形状的极限轮廓。在这个建议中,我们考虑了许多关于方程(*)的问题,并讨论了(*)的结果可能推广到更一般的方程类。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
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Roger Nussbaum其他文献
Periodic points of positive linear operators and Perron-Frobenius operators
- DOI:
10.1007/bf01192149 - 发表时间:
2001-03-01 - 期刊:
- 影响因子:0.900
- 作者:
Roger Nussbaum - 通讯作者:
Roger Nussbaum
Roger Nussbaum的其他文献
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{{ truncateString('Roger Nussbaum', 18)}}的其他基金
Topics in Nonlinear Functional Differential Equations and the Computation of Hausdorff Dimension
非线性泛函微分方程与Hausdorff维数计算专题
- 批准号:
1201328 - 财政年份:2012
- 资助金额:
$ 7.5万 - 项目类别:
Continuing Grant
Topics in Nonlinear Functional Differential Equations
非线性函数微分方程主题
- 批准号:
0701171 - 财政年份:2007
- 资助金额:
$ 7.5万 - 项目类别:
Standard Grant
Cone-Preserving Operators and Nonlinear Differential-Delay Equations
保锥算子和非线性微分时滞方程
- 批准号:
0401100 - 财政年份:2004
- 资助金额:
$ 7.5万 - 项目类别:
Standard Grant
Topics in Nonlinear Difference and Differential-Delay Equations
非线性差分和微分时滞方程主题
- 批准号:
0070829 - 财政年份:2000
- 资助金额:
$ 7.5万 - 项目类别:
Continuing Grant
U.S.- France Cooperative Research(INRIA): Control of Oscillations
美法合作研究(INRIA):振荡控制
- 批准号:
0001522 - 财政年份:2000
- 资助金额:
$ 7.5万 - 项目类别:
Standard Grant
Boundary Layer Phenomena and Periodic Solutions for Functional Differential Equations
泛函微分方程的边界层现象和周期解
- 批准号:
9706891 - 财政年份:1997
- 资助金额:
$ 7.5万 - 项目类别:
Continuing Grant
Mathematical Sciences: Boundary Layer Phenomena for Nonlinear Functional Differential Equations
数学科学:非线性泛函微分方程的边界层现象
- 批准号:
9105930 - 财政年份:1991
- 资助金额:
$ 7.5万 - 项目类别:
Continuing Grant
Mathematical Sciences: Boundary Layer Phenomena for Functional Differential Equations and Means and Their Iterations
数学科学:泛函微分方程和均值及其迭代的边界层现象
- 批准号:
8903018 - 财政年份:1989
- 资助金额:
$ 7.5万 - 项目类别:
Continuing Grant
Mathematical Sciences: Nonlinear Functional Analysis
数学科学:非线性泛函分析
- 批准号:
8803495 - 财政年份:1988
- 资助金额:
$ 7.5万 - 项目类别:
Standard Grant
Mathematical Sciences: Boundary Layer Phenomena for Singularly Perturbed Differential-Delay Equations
数学科学:奇异摄动微分时滞方程的边界层现象
- 批准号:
8713998 - 财政年份:1987
- 资助金额:
$ 7.5万 - 项目类别:
Standard Grant
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