NONUNIQUENESS OF SOLUTIONS OF A DEGENERATE PARABOLIC EQUATION

We give some results about nonuniqueness of the solutions of the Cauchy problem for a class of nonlinear degenerate parabolic equations arising in several applications in biology and physics. This phenomenon is a truly nonlinear one and occurs because of the degeneracy of the equation at the points where u = 0. For a given set of values of the parameter involved, we prove that there exists a one parameter,family of weak solutions; moreover, restricting the parameter set, nonuniqueness appears even in the class of classical solutions.