Nonlinear partial differential equations in heterogeneous frameworks

异构框架中的非线性偏微分方程

• 批准号: RGPIN-2017-04313
• 负责人: ElSmaily, Mohammad
• 金额: $ 1.02万
• 依托单位: University of New Brunswick
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635312
• 关键词: Nonlinear; partial; differential; equations; heterogeneous

My proposed research deals with the deterministic analysis of certain partial differential equations (PDEs) in heterogeneous frameworks. The first part of the proposal is devoted to reaction-advection-diffusion equations with coefficients that depend on space/time variables in domains with perforations. Although some mathematical milestones in the theory of parabolic PDEs date back to the 1930’s, the setting considered until the year 2000 was relatively homogeneous: semi-linear parabolic equations with constant diffusion and no drift. That is where those PDEs exhibit traveling wave solutions.

我建议的研究涉及某些偏微分方程（PDE）在异构框架的确定性分析。建议的第一部分是专门的反应对流扩散方程的系数取决于空间/时间变量的域穿孔。虽然抛物型偏微分方程理论中的一些数学里程碑可以追溯到20世纪30年代，但直到2000年，所考虑的设置都是相对均匀的：具有常数扩散和无漂移的半线性抛物方程。这就是这些偏微分方程表现出行波解的地方。