Instantaneous Shrinking of the Support of Energy Solutions

The Cauchy problem for a class of nonlinear diffusion-reaction equations is studied. The equations may be classified as being of degenerate parabolic type. It is shown that under certain conditions solutions of the problem exhibit instantaneous shrinking. This is to say, at any positive time the spatial support of the solution is bounded above, although the support of the initial data function is not. We also provide some estimates of the behavior of the free boundary