Mathematical Sciences: Exterior Problems, Nonlinear Elasticity and Stochastic Evolution Problems

数学科学：外部问题、非线性弹性和随机演化问题

• 批准号: 9002562
• 负责人: Victor Mizel
• 金额: $ 12.65万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002562&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Exterior; Problems; Nonlinear

This project has two parts. Part A involves work in nonlinear partial differential equations and the calculus of variations (Exterior Domain Problems, Prescribed Mean Curvature Problems and Perturbation of even Functionals, Lavrentiev gap, Lavrentiev envelope, homogeneous materials with layered microstructure, gradients with no rank-one connections). Part B deals with stochastic control and stochastic analysis (Bolza problems, Boundary value problems with noise, Kolmogorov differential equations). Most of these problems attempt to answer questions in engineering and physical sciences.

该项目有两个部分。 A 部分涉及非线性偏微分方程和变分法（外域问题、规定平均曲率问题和偶泛函的摄动、拉夫连季耶夫间隙、拉夫连季耶夫包络、具有分层微观结构的均质材料、没有一级连接的梯度）。 B 部分涉及随机控制和随机分析（Bolza 问题、噪声边界值问题、Kolmogorov 微分方程）。 这些问题大多数试图回答工程和物理科学中的问题。