Mathematical Sciences: Asymptotic and Singular Perturbation Methods for Bifurcation and Moving Boundary Problems with Applications

数学科学：分岔和移动边界问题的渐近奇异摄动方法及其应用

• 批准号: 9001402
• 负责人: Thomas Erneux
• 金额: $ 4.94万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001402&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Asymptotic; Singular; Perturbation

With this award the principal investigator will continue his application of asymptotic methods of singular perturbation type to the study of bifurcation problems and moving boundary problems that arise from reaction-diffusion systems. In particular, he will investigate so-called singular bifurcation problems, wherein small changes in the bifurcation parameter can cause large responses in the system, laser instabilities, and the changing time history of the moving interface in certain pharmaceutical problems involving the time-release of medication. This proposal is concerned with bifurcation phenomena. As an illustration, stand a plastic ruler on its end and push on the top end. If you do not push very hard nothing happens. But if you push sufficiently hard the first thing that happens is that the ruler bows, either to the left or to the right. We call this a bifurcation: the configuration of the straight ruler has split (bifurcated) into one of two possible shapes. Applying still more force to the ruler results in an even number of bowed shapes having more and more curves. The principal investigator will study the number of solutions that bifurcate from a given solution of systems of equations that govern lasers and release of chemicals in the body.

凭借这一奖项，首席研究员将继续他的 奇异摄动型渐近方法的应用 分支问题和动边界问题的研究 由反应扩散系统产生的。 他特别 将研究所谓的奇异分叉问题，其中 分叉参数的微小变化可以引起大的 系统中的响应，激光不稳定性，以及 在某些药物中移动界面的时间历程 涉及药物释放时间的问题。这项建议 与分叉现象有关。 作为说明， 把一把塑料尺立在它的一端，然后推它的顶端。 如果你 不要太用力，什么也不会发生。 但如果你逼 足够硬的第一件事就是统治者 向左或向右鞠躬。 我们称之为 分叉：直尺的配置已分裂 （分叉的）两种可能的形状之一。 仍在应用 对标尺施加更大的力会产生偶数个弓形 曲线越来越多。 主要研究者将 研究从一个给定解分支出来的解的个数。 控制激光和释放的方程组的解 体内的化学物质。