  We study the evolution of fronts in a bistable reaction-diffusion system when
the nonlinear reaction term is spatially non-homogeneous. This equation has
been used to model wave propagation in various biological systems. Extending
previous works on homogeneous reaction terms, we derive asymptotically an
equation governing the front motion, which is strongly nonlinear and, for the
two-dimensional case, generalizes the classical mean curvature flow equation.
We study the motion of one- and two- dimensional fronts, finding that the
non-homogeneity acts as a "potential function" for the motion of the front;
i.e., there is wave propagation failure and the steady state solution depends
on the structure of the function describing the non-homogeneity.
