Large fronts in hydrodynamics and nonlinear elasticity

Abstract: In this talk, we will present some new abstract results on global bifurcation theory for front-type solutions to (fully nonlinear) elliptic PDE posed on infinite cylinders.  These problems arise in a variety of physical and mathematical settings.  Specifically, we will discuss the existence of large-amplitude hydrodynamics bores, which are traveling front solutions to the two-phase free boundary Euler equations.  A second application will be to nonlinear elasticity, where we study non-perturbative anti-plane shear equilibria.

This is joint work with Robin Ming Chen and Miles H. Wheeler.