Fluid and Solid Mechanics
Many engineering problems
involving the deformation of elastic solids or the
flow of fluid in various physical configurations
result in nonlinear boundary value problems involving ordinary and
partial differential equations. My work involves
answering questions of
existence and uniqueness of solutions for such problems and
qualitative behavior of the solutions. Much of the work
involving fluid mechanics is done in collaboration with
Patrick Weidman at the University of Colorado.
The work involving solid mechanics is done
in collaboration with Debra Polignone-Warne
and Paul Warne at James Madison University.
The areas of mathematics
involved include ordinary and partial differential equations,
dynamical systems theory, and topology.