Mathematical Sciences: Elliptic and Parabolic Problems from Physical Models

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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. ***