Mathematical Sciences: Qualitative Behavior of Solutions to Nonlinear Problems in Elasticity

点击翻译按钮获取中文摘要

The principal investigator will study the qualitative behavior of solutions to a class of problems from multidimensional elasticity. The problems to be considered are equilibrium problems for realistic models of homogeneous, isotropic, hyperelastic materials in two and three dimensions. In particular, the stored energy functions in these problems blow up as the determinant of the deformation gradient approaches zero. The main goal of the project is to determine a priori regularity and qualitative behavior of solutions. The principal investigator will also investigate uniqueness of solutions as well as qualitative properties of solutions to specific boundary value problems, such as the one describing uniaxial extension of a hyperelastic bar.