EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A CLASS OF QUASILINEAR DEGENERATE PARABOLIC EQUATIONS

2019 ◽  
Vol 64 (6) ◽  
pp. 3-11
Author(s):  
Chi Tran Thi Quynh ◽  
Thuy Le Thi
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Degenerate Parabolic Equations ◽  
Uniqueness Of Solutions ◽  
Degenerate Parabolic

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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