Existence and uniqueness of a renormalized solution for nonlinear degenerate parabolic equations with diffuse measure data

2019 ◽  
Vol 190 (2) ◽  
pp. 245-260 ◽  
Author(s):  
A. Bouajaja ◽  
A. Marah ◽  
H. Redwane
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Degenerate Parabolic Equations ◽  
Measure Data ◽  
Renormalized Solution ◽  
Diffuse Measure ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

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

2021 ◽  
Vol 14 (1) ◽  
pp. 204-233
Author(s):  
Quincy Stevene Nkombo ◽  
Fengquan Li
Keyword(s):  
Parabolic Equations ◽  
Radon Measure ◽  
Degenerate Parabolic Equations ◽  
Measure Data ◽  
Initial Value ◽  
Parabolic Capacity ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Strongly Degenerate ◽  
Nonlinear Degenerate

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.

scholarly journals Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

2005 ◽  
Vol 2005 (6) ◽  
pp. 607-617 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Parabolic Partial Differential Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

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