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- Title
L<sup>2</sup>-Estimates for Homogenization of Diffusion Operators with Unbounded Nonsymmetric Matrices.
- Authors
Pastukhova, S. E.
- Abstract
In the space ℝd, d ≥ 2, we study the diffusion equation −div (∇uε +b(x/ε)∇uε)+uε = f ∈L2(ℝd), u∈H1(ℝd), where b(y) is an unbounded 1-periodic skew symmetric matrix and ε is a small parameter. The matrix b(y) is assumed to be integrable with respect to the period with exponent s, where s = d for d ≥ 3 and s > 2 for d = 2. Assuming that a solution to the diffusion equation is not necessarily unique, we find an asymptotics for the so-called approximate resolvent with remainder of order ε2 as ε → 0.
- Subjects
NONSYMMETRIC matrices; HEAT equation; SYMMETRIC matrices; EXPONENTS; ASYMPTOTIC homogenization
- Publication
Journal of Mathematical Sciences, 2022, Vol 268, Issue 4, p473
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-022-06207-x