Summary
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.
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Bertsch, M., Dal Passo, R. & Ughi, M. Nonuniqueness of solutions of a degenerate parabolic equation. Annali di Matematica 161, 57–81 (1992). https://doi.org/10.1007/BF01759632
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DOI: https://doi.org/10.1007/BF01759632