Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Convergence of bi-spatial pullback random attractors and stochastic Liouville type equations for nonautonomous stochastic p-Laplacian lattice system (2406.07192v2)

Published 11 Jun 2024 in math.PR and math.AP

Abstract: We consider convergence properties of the long-term behaviors with respect to the coefficient of the stochastic term for a nonautonomous stochastic $p$-Laplacian lattice equation with multiplicative noise. First, the upper semi-continuity of pullback random $(\ell2,\ellq)$-attractor is proved for each $q\in[1,+\infty)$. Then, a convergence result of the time-dependent invariant sample Borel probability measures is obtained in $\ell2$. Next, we show that the invariant sample measures satisfy a stochastic Liouville type equation and a termwise convergence of the stochastic Liouville type equations is verified. Furthermore, each family of the invariant sample measures is turned out to be a sample statistical solution, which hence also fulfills a convergence consequence.

Summary

We haven't generated a summary for this paper yet.