Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity

2008 ◽  
Vol 150 (5) ◽  
pp. 2289-2301 ◽  
Author(s):  
S. N. Antontsev ◽  
S. I. Shmarev
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Degenerate Parabolic Equations ◽  
Variable Exponents ◽  
Uniqueness Of Solutions ◽  
Degenerate Parabolic

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

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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