Instantaneous Shrinking in Nonlinear Diffusion-convection

  title={Instantaneous Shrinking in Nonlinear Diffusion-convection},
  author={Brian H. Gilding and Robert Kersner and Barbara L. Keyfitz},
The Cauchy problem for a nonlinear diffusion-convection equation is studied. The equation may be classified as being of degenerate parabolic type with one spatial derivative and a time derivative. It is shown that under certain conditions solutions of the initial-value 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. This is a phenomenon which is normally… CONTINUE READING