  An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk
n-GaAs with circular contacts is presented. A moving pulse far from contacts is
approximated by a moving free boundary separating regions where the electric
potential solves a Laplace equation with subsidiary boundary conditions. The
dynamical condition for the motion of the free boundary is a Hamilton-Jacobi
equation. We obtain the exact solution of the free boundary problem (FBP) in
simple one-dimensional and axisymmetric geometries. The solution of the FBP is
obtained numerically in the general case and compared with the numerical
solution of the full system of equations. The agreement is excellent so that
the FBP can be adopted as the basis for an asymptotic study of the
multi-dimensional Gunn effect.
