Radon Measure-valued Solutions for Nonlinear Strongly Degenerate Parabolic Equations with Measure Data
Keywords:Radon measure-valued solutions, Nonlinear degenerate parabolic equations, Capacity
AbstractIn this paper, we prove the existence of Radon measure-valued solutions for nonlinear degenerate parabolic equations with nonnegative bounded Radon measure data. Moreover, we show the uniqueness of the measure-valued solutions when the Radon measure as a forcing term is diffuse with respect to the parabolic capacity and the Radon measure as a initial value is diffuse with respect to the Newtonian capacity. We also deduce that the concentrated part of the solution with respect to the Newtonian capacity depends on time.
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