Open AccessRadon Measure-valued Solutions for Nonlinear Strongly Degenerate Parabolic Equations with Measure Data
Author(s) -
Quincy Stévène Nkombo,
Fengquan Li
Publication year - 2021
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v14i1.3877
Subject(s) - radon measure , mathematics , measure (data warehouse) , uniqueness , degenerate energy levels , radon , bounded function , mathematical analysis , parabolic partial differential equation , nonlinear system , forcing (mathematics) , partial differential equation , pure mathematics , physics , locally compact space , quantum mechanics , database , computer science
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.