Mathematical Sciences: Topics On Regularity Theory and Free Boundary Problems

数学科学：正则性理论和自由边界问题专题

• 批准号: 8802883
• 负责人: Emmanuele DiBenedetto
• 金额: $ 8.76万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-05-15 至 1991-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802883&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Regularity; Theory

Laws of Conservation of mass, energy and other physical quantities in the study of fluids and materials can be written as partial differential equations. Realistic models generally lead to nonlinear equations which are often degenerately or singularly parabolic, depending on the physical situation. Whereas the linear theory is well established the nonlinear theory is not. This project will study the smoothness and qualitative behavior of solutions to degenerate and singular parabolic equations.

质量、能量和其他物理量的守恒定律 流体和材料研究中的量可以写为 偏微分方程 现实模型通常会导致 到非线性方程，通常是退化的或奇异的 抛物线，取决于实际情况。 而 线性理论已经很好地建立起来，而非线性理论还没有。 本项目将研究平滑性和定性行为 退化和奇异抛物方程的解。