Mathematical Sciences: Diffusion Models for Heterogeneous Media

数学科学：异质介质的扩散模型

• 批准号: 8801264
• 负责人: Ralph Showalter
• 金额: $ 7.99万
• 依托单位: University of Texas at Austin
• 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: 1988-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801264&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Diffusion; Models; Heterogeneous

A quasilinear system of partial differential equations is shown to be a general model for diffusion in heterogeneous media. The system to be studied may contain very nonlinear singular or degenerate coefficients and include certain free-boundary problems that arise in various applications. The objective is to find sufficient conditions to guarantee the initial-boundary- value problem is well-posed, to investigate and compare the properties of solutions in relevant special cases, and to study the dependence of solutions on parameters or functions in the equations.

偏微分方程的拟线性系统被证明是异质介质中扩散的通用模型。 要研究的系统可能包含非常非线性的奇异或简并系数，并包括各种应用中出现的某些自由边界问题。 目的是找到保证初始边值问题适定的充分条件，研究和比较相关特殊情况下解的性质，并研究解对方程中参数或函数的依赖性。