Stochastic Homogenization of Parabolic Equations with Lower-order Terms

2024/08/22 by Man Yang, Yang, Man
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2408.12204

openalex publication_date 2024/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The study of homogenization results has long been a central focus in the field of mathematical analysis, particularly for equations without lower-order terms. However, the importance of studying homogenization results for parabolic equations with lower-order terms cannot be understated. In this study, we aim to extend the analysis to homogenization for the general parabolic equation with random coefficients: ∂_tp^ε-∇⋅(a( \dfracxε,\dfractε²)∇ p^ε)-b( \dfracxε,\dfractε²)∇ p^ε-d( \dfracxε,\dfractε²) p^ε=0. Moreover, we establish the Caccioppoli inequality and Meyers estimate for the generalized parabolic equation. By using the generalized Meyers estimate, we get the weak convergence of p^ε in H¹.

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