Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Let O ⊃ ℝd be a bounded domain of class C1,1. In L2(O;n), a selfadjoint matrix second order elliptic differential operator BD,ε, 0 < ε ≤ 1, is considered with the Dirichlet boundary condition. The principal part of the operator is given in a factorized form. The operator involves first and zero order terms. The operator BD,ε is positive definite; its coefficients are periodic and depend on x/ε. The behavior of the operator exponential e -BD,εt, t > 0, is studied as ε → 0. Approximations for the exponential e -BD,εt are obtained in the operator norm on L2(O;n) and in the norm of operators acting from L2(O;n) to the Sobolev space H1(O;n). The results are applied to homogenization of solutions of the first initial boundary-value problem for parabolic systems.
Язык оригинала | английский |
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Страницы (с-по) | 935-978 |
Журнал | St. Petersburg Mathematical Journal |
Том | 29 |
Номер выпуска | 6 |
DOI | |
Состояние | Опубликовано - 1 янв 2018 |
ID: 36545065