Mathematical Sciences: Spatial and Temporal Nonlinear Integral and Differential Equations

数学科学：时空非线性积分和微分方程

• 批准号: 9002028
• 负责人: Bard Ermentrout
• 金额: $ 17.68万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002028&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Spatial; Temporal; Nonlinear

This project will attempt to the analysis of neural nets to incorporate synaptic delay and also use recent results to analyze large amplitude behavior of simple neural nets. The behavior large numbers of coupled nonlinear oscillators will be analyzed as a model for synchrony. Models of aggregation and branching will be studied both numerically and analytically. Work on models for corticotopic maps will continue. Most of the problems involve nonlinear integro-differential equations and how they apply to biological phenomena. The PI's will also continue their studies of a nonlinear fourth order boundary value problem which models fluid flow past a stretching sheet. In addition studies of second order semilinear elliptic equations will be continued. In particular the question of uniqueness of solutions with prescribed numbers of zeros will be addressed. Finally, finite time blow-up in Schrodinger's equation will be investigated.

这个项目将尝试分析神经网络以包含突触延迟，并使用最新的结果来分析简单神经网络的大幅度行为。将大量耦合的非线性振子的行为作为同步的模型进行分析。我们将从数值和解析两方面研究聚集和分支的模型。皮质地形图模型的工作将继续进行。大多数问题涉及到非线性积分-微分方程组以及它们如何应用于生物现象。PI还将继续他们对一个非线性四阶边值问题的研究，该问题模拟了流过拉伸薄板的流体流动。此外，我们还将继续研究二阶半线性椭圆型方程。特别是，将讨论具有规定零数的解的唯一性问题。最后，我们将研究薛定谔方程的有限时间爆破。