Mathematical Sciences: Spatial and Temporal Patterns in Non-Linear Differential Equations

数学科学：非线性微分方程中的空间和时间模式

• 批准号: 8701405
• 负责人: Bard Ermentrout
• 金额: $ 12.97万
• 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: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701405&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Spatial; Temporal; Patterns

The investigators will continue their studies over the last several years of pattern formation in biological systems and the behavior of nonlinear equations in fluid mechanics. Their joint work includes extending a recent theorem which proves the existence of oscillatory solutions in an inhomogeneous reaction diffusion equation. They will also extend their recent studies of a fourth order nonlinear differential equation which arises in boundary layer theory in fluid mechanics. Professor Ermentrout will continue his joint research work with Professor Nancy Kopell of Boston University on the behavior of aggregates of coupled oscillators. He will also continue his joint research work on molluscan pigmentation patterns with Professor George Oster of University of California at Berkeley and work on fungal growth with Professor Leah Edelstein of Duke University. Professor Troy will extend his recent investigations of a reaction diffusion equation arising in chemical reactor and combustion theory. Depending on the values of physical parameters in the model, the solutions exhibit a variety of possible behavior ranging from finite time "blow-up" to finite time "extinction". He will continue his investigations of the behavior of self similar solutions which are used in analyzing the asymptotics of both the blow-up and extinction processes. This research falls into the general area of applied mathematical analysis, with potential applications to chemistry and biology.

调查人员将在过去几年继续他们的研究 多年的模式形成的生物系统和行为的 流体力学中的非线性方程 他们的共同工作包括 推广了最近的一个定理，该定理证明了振荡的存在性， 非齐次反应扩散方程的解 他们将 还扩展了他们最近对四阶非线性 流体边界层理论中的微分方程 力学 Ermentrout教授将继续他的联合研究工作， 波士顿大学的南希·科佩尔教授对 耦合振荡器的集合体。 他还将继续他的联合 与乔治教授一起研究软体动物的色素沉着模式 加州大学伯克利分校的奥斯特和真菌生长的工作 杜克大学的莉亚埃德尔斯坦教授。 特洛伊教授将把他最近对一种反应的研究 化学反应器中的扩散方程和燃烧理论。 根据模型中物理参数的值， 解表现出各种可能的行为， 时间“爆炸”到有限时间“灭绝”。 他将继续他的 研究了自相似解的行为， 在分析爆炸和灭绝的渐近性时， 流程. 本研究福尔斯应用数学的一般范畴 分析，具有化学和生物学的潜在应用。