Mathematical Sciences: Elliptic and Parabolic Problems from Physical Models

9623438首席研究员鲍曼将从二维和三维空间的物理模型研究椭圆型和抛物型偏微分方程组(具有实际的初始和边界条件)。特别是，我们将研究描述受外加磁场影响的超导材料中的电流和磁场的Ginzburg-Landau系统。首席研究员还将根据材料科学家开发的模型研究描述超弹性材料的非线性系统。上述问题涉及材料行为的实际数学模型，这些模型在材料工程、材料科学、机械工程和物理中具有实际意义。需要研究的问题包括外场的模数如何影响超导材料中的电流和磁场，以及材料中的缺陷和不均匀如何影响其超导电性。这种性质的问题在应用中很重要，例如在使用超导材料进行电力传输和使用液晶显示复杂的内部信息方面。***

9623438 Bauman The principal investigator will study elliptic and parabolic systems of partial differential equations (with physically realistic initial and boundary conditions) from physical models in two and three space dimensions. In particular, the Ginzburg-Landau system describing the current and magnetic field in a superconducting material subject to an external magnetic field will be studied. The principal investigator will also study nonlinear systems describing hyperelastic materials based on models developed by materials scientists. %%% The above problems concern realistic mathematical models for the behavior of materials which are of practical interest in materials engineering, materials science, mechanical engineering, and physics. Issues to be studied include how the modulus of the external field affects current and magnetic field in a superconducting material, and how defects and inhomogeneities in a material affect its superconductivity. Problems of this nature are important in applications such as in the use of superconducting materials for power transmission and the use of liquid crystals for displaying complex internal information. ***