Mathematical Sciences: Semilinear Partial Differential Equations and Their Applications

数学科学：半线性偏微分方程及其应用

• 批准号: 9305658
• 负责人: Xuefeng Wang
• 金额: $ 3.5万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305658&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Semilinear; Partial; Differential

Research will be performed in three areas: (i) stability, finite time blow-up, decay rates, and asymptotics of life span of solutions to reaction-diffusion equations in the whole space; (ii) locations and rates of blow-up of solutions to spatially non-uniform nonlinear heat equations (model equations including the ones arising in the channel flow problem); (iii) concentration phenomena of solutions of semilinear elliptic equations (including Schrodinger equations and the equations arising in chemotaxis and binary mixture problems in biology and physics). The problems proposed are of mathematical, physical and biological importance. Some of the equations in the project have been well-known to mathematicians for years, yet new and challenging questions about these equations remain unanswered. The solutions for these problems will not only deepen our understanding of these concrete models, but also have impact on the understanding of and resolution to other related problems in the fields of mathematics, physics and biology.

研究将在三个领域进行：（i）稳定性，有限的时间爆炸，衰减率和渐近的寿命跨度溶液的寿命跨度对反应扩散方程的寿命跨度； （ii）对空间非均匀非线性热方程（包括在通道流问题中产生的模型方程）的溶液的位置和爆炸速率； （iii）半线性椭圆方程的溶液浓度现象（包括生物学和物理学中的趋化性和二元混合物问题）的溶液（包括schrodinger方程和方程）。 提出的问题是数学，物理和生物学重要性。 多年来，该项目中的某些方程式一直是数学家众所周知的，但是有关这些方程式的新问题仍然没有得到答案。 这些问题的解决方案不仅会加深我们对这些具体模型的理解，而且还会影响对数学，物理学和生物学领域其他相关问题的理解和解决方案。