Return to Mathematical Applications List for David Ross
This problem involved the solution of scalar conservation laws, like the well-known Burger's equation, but with non-convex flux functions. Such problems are usually initial-value problems, but in this application, the problems are moving boundary problems, like the Stefan problem for parabolic equations. The modeling of the problem involved the derivation of entropy conditions to single out physically realistic conditions on the moving boundaries.
A thin sheet of metal is coated on a thick polymer base. When the system is perturbed, waves travel through it, waves in the metal sheet and waves in the polymer are coupled. The waves in the polymer are described by the equations of incompressible linear elasticity, the waves in the metal satisfy a nonlinear mixed-type PDE, a PDE that is hyperbolic when the metal is stretched, elliptic when it is compressed.
How does one measure the imbalance of color in a photographic system? This problem involved using geometry and linear algebra to project three-dimensional color space onto a two-dimensional subspace, and using multivariate normal statistical distributions in that subspace to determine a measure of color imbalance.