Mathematical Sciences: Dynamical Systems with Infinitely Many Degrees of Freedom in Mathematical Physics

数学科学：数学物理中具有无限多个自由度的动力系统

• 批准号: 9203359
• 负责人: Clarence Wayne
• 金额: $ 7.5万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203359&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Systems; Infinitely

This proposal is concerned with the dynamics of some partial differential equations that arise in mathematical physics. Problems concerning the method of accelerated convergence, KAM theory, center manifolds, and normal forms are complicated in the finite dimensional case. In infinite dimensions there are additional complications such as the appearance of zero divisors rather that just small divisors. Dynamical systems is a geometric rigorous way of describing the behavior of solutions of systems of ordinary or partial differential equations which can not be solved explicitly. The ability to accurately describe the behavior of such solutions has important ramifications in understanding the world around us.

该建议与数学物理学中某些部分微分方程的动态有关。 在有限的维度情况下，有关加速收敛，KAM理论，中心歧管和正常形式的方法的问题是复杂的。 在无限的维度中，还有其他并发症，例如零除数的外观，而只是小除数。 动力系统是描述无法明确求解的普通或部分微分方程系统解决方案的行为的几何严格方式。 准确描述这种解决方案的行为的能力在理解我们周围的世界方面具有重要的影响。