含有旋度算子的变分问题和非线性偏微分方程组

项目名称： 含有旋度算子的变分问题和非线性偏微分方程组

项目编号： No.10871071

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 潘兴斌

作者单位： 华东师范大学

项目金额： 24万元

中文摘要： 本项目研究含有旋度算子的变分问题与非线性偏微分方程组。主要研究含有旋度算子的泛函在逐点约束条件下的变分问题，含有旋度算子的拟线性椭圆型偏微分方程组，以及相关的数学问题。本项目注重研究区域的拓扑与几何性质对这些变分问题与偏微分方程组的解的影响。所研究的问题在科学技术领域中有着广泛的应用背景。我们将深入研究一些关键的数学问题，建立基本理论，并用以解决科学技术中的有关数学问题。

中文关键词： 旋度算子；变分学；非线性椭圆型偏微分方程组

英文摘要： The main topics of this project are variational problems and nonlinear partial differential systems involving the operator curl. The investigators will study the variational problems of functionals containing the curl operator for vector fields subjected to some pointwise constrain conditions; study quasilinear elliptic partial differential systems involving the operator curl, and study the related mathematical problems. This project emphasizes the investigation of the effect of the topological and geometric properties of the underlying domains on the behavior of the minimizers of the variational problems and the solutions of the partial differential systems involving the operator curl. Most of the research topics studied in this project have definite background and possible applications in sciences and technology. In this project the investigators will study a series of key problems in mathematics, establish basic theory in this field, and solve related mathematical problems arising in science and technology.

英文关键词： operator curl; variational problems; nonlinear elliptic partial differential systems