TITLE:
Weak Pullback Attractors of Stochastic Semilinear Degenerate Equations with Memory Driven by Nonlinear Noise
AUTHORS:
Ximeng Liu
KEYWORDS:
Semilinear Degenerate Equation, Weak Pullback Mean Random Attractor, Nonlinear Noise, Memory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
10,
2025
ABSTRACT: This paper is concerned with the long-time behavior of solutions for a class of stochastic semilinear degenerate equations with memory driven by nonlinear noise on
ℝ
n
. We primarily provide sufficient conditions for studying such problems, including the degenerate term
div{
a(
x
)∇u }
, nonlinear drift, and diffusion terms. Based on these conditions, we establish the existence of weakly compact pullback absorbing sets and further obtain the existence and uniqueness of weak
D
-pullback mean random attractors.