Radon Measure-valued Solutions for Nonlinear Strongly Degenerate Parabolic Equations with Measure Data

Quincy Stevene Nkombo, Fengquan Li

Abstract

In 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.

Keywords

Radon measure-valued solutions, Nonlinear degenerate parabolic equations, Capacity

Full Text:

PDF