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

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.

Application of the SBA Method to Solve the Nonlinear Biological Population Models

This paper presents numerical solution of some nonlinear degenerate parabolic equations arising in the spatial di¤usion of biological populations. The SBA method based on combination of Adomian decomposition method, principle of Picard and successive approximations is used for solving these equations. The analytical obtained solutions show that the SBA method leads to more accurate results.