scholarly journals Existence and uniqueness of entropy solutions to strongly degenerate parabolic equations with discontinuous coefficients

2013 ◽  
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Discontinuous Coefficients ◽  
Entropy Solutions ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Strongly 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.

Wong–Zakai approximations and attractors for stochastic degenerate parabolic equations on unbounded domains

2020 ◽  
pp. 2150033
Author(s):  
Fahe Miao ◽  
Hui Liu ◽  
Jie Xin
Keyword(s):  
White Noise ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Stationary Process ◽  
Unbounded Domains ◽  
Degenerate Parabolic Equations ◽  
Pullback Attractors ◽  
Multiplicative White Noise ◽  
Degenerate Parabolic

The Wong–Zakai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered in this paper. We first establish the existence and uniqueness of tempered pullback attractors for the Wong–Zakai approximations of stochastic degenerate parabolic equations. We then prove that the attractors of Wong–Zakai approximations converge to the attractor of stochastic degenerate parabolic equations driven by multiplicative white noise.

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