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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 homog...enization 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: ∂_t p^𝜖 − ∇⋅(a(𝑥/𝜖, 𝑡/𝜖^2)∇p^𝜖) − b(𝑥/𝜖, 𝑡/𝜖^2)∇p^𝜖 − d(𝑥/𝜖, 𝑡/𝜖^2)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 H^1.続きを見る
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Mendeley出力
