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Laminated Metamaterials - Divergence Form Equations and Homogenisation

Offered By: Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube

Tags

Metamaterials Courses Partial Differential Equations Courses Quantum Theory Courses Mathematical Physics Courses Spectral Theory Courses

Course Description

Overview

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Explore divergence form equations with sign-indefinite, real-valued coefficients in d dimensions in this 23-minute talk from the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" at the Erwin Schrödinger International Institute. Discover solution criteria for the induced divergence-form problem in L_2 and learn how, for any given piecewise constant coefficient α depending on x_1, there exists only a countable, nowhere dense set Λ⊆ℝ where div(α-λ)grad fails to be continuously invertible in L_2. Examine homogeneous Dirichlet boundary conditions on the boundary of Ω=(0,1)×Ω̂, with Ω̂⊆ℝ^(d-1) open and bounded. Delve into an associated homogenisation problem and a generalised homogenisation method for highly oscillatory ill-posed problems. Understand how homogenised coefficients can lead to 4th order nonlocal operators in certain cases, despite starting with second-order, local problems. Based on arXiv:2210.04650, this talk by Marcus Waurick provides insights into laminated metamaterials and their mathematical properties.

Syllabus

Marcus Waurick - Laminated Metamaterials


Taught by

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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