Nonlocal H-convergence

Waurick, Marcus (2018) Nonlocal H-convergence. Calculus of Variations and Partial Differential Equations, 57. 159. ISSN 1432-0835 (https://doi.org/10.1007/s00526-018-1436-5)

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Abstract

We introduce the concept of nonlocal H-convergence. For this we employ the theory of abstract closed complexes of operators in Hilbert spaces. We show uniqueness of the nonlocal H-limit as well as a corresponding compactness result. Moreover, we provide a characterisation of the introduced concept, which implies that local and nonlocal H-convergence coincide for multiplication operators. We provide applications to both nonlocal and nonperiodic fully time-dependent 3D Maxwell's equations on rough domains. The material law for Maxwell's equations may also rapidly oscillate between eddy current type approximations and their hyperbolic non-approximated counter parts. Applications to models in nonlocal response theory used in quantum theory and the description of meta-materials, to fourth order elliptic problems as well as to homogenisation problems on Riemannian manifolds are provided.

ORCID iDs

Waurick, Marcus ORCID logoORCID: https://orcid.org/0000-0003-4498-3574;
  • Item type:Article
    ID code:65713
    Dates:
    Date
    Event
    30 December 2018
    Published
    29 September 2018
    Published Online
    7 September 2018
    Accepted
    Notes:This is a pre-print of an article published in Calculus of Variations and Partial Differential Equations. The final authenticated version is available online at: https://doi.org/10.1007/s00526-018-1436-5
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:08 Oct 2018 13:52
    Last modified:21 Nov 2024 01:15
    URI:https://strathprints.strath.ac.uk/id/eprint/65713
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