Uniform boundary controllability and homogenization of wave equations

Fanghua Lin; Zhongwei Shen

doi:10.4171/JEMS/1137

Uniform boundary controllability and homogenization of wave equations

Fanghua Lin, Zhongwei Shen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is uniform in ∈ (the scale of the microstructure) for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less than C∈-2=3.

Original language	English (US)
Pages (from-to)	3031-3053
Number of pages	23
Journal	Journal of the European Mathematical Society
Volume	24
Issue number	9
DOIs	https://doi.org/10.4171/JEMS/1137
State	Published - 2022

Keywords

Boundary controllability
convergence rate
homogenization
oscillating coefficient
wave equation

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/JEMS/1137

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title = "Uniform boundary controllability and homogenization of wave equations",

abstract = "We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is uniform in ∈ (the scale of the microstructure) for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less than C∈-2=3.",

keywords = "Boundary controllability, convergence rate, homogenization, oscillating coefficient, wave equation",

author = "Fanghua Lin and Zhongwei Shen",

note = "Funding Information: Funding. Research supported in part by NSF grant DMS-1501000. Research of Zhongwei Shen supported in part by NSF grant DMS-1600520. Publisher Copyright: {\textcopyright} 2022 European Mathematical Society Publishing House. All rights reserved.",

year = "2022",

doi = "10.4171/JEMS/1137",

language = "English (US)",

volume = "24",

pages = "3031--3053",

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T1 - Uniform boundary controllability and homogenization of wave equations

AU - Lin, Fanghua

AU - Shen, Zhongwei

N1 - Funding Information: Funding. Research supported in part by NSF grant DMS-1501000. Research of Zhongwei Shen supported in part by NSF grant DMS-1600520. Publisher Copyright: © 2022 European Mathematical Society Publishing House. All rights reserved.

PY - 2022

Y1 - 2022

N2 - We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is uniform in ∈ (the scale of the microstructure) for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less than C∈-2=3.

AB - We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is uniform in ∈ (the scale of the microstructure) for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less than C∈-2=3.

KW - Boundary controllability

KW - convergence rate

KW - homogenization

KW - oscillating coefficient

KW - wave equation

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SP - 3031

EP - 3053

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 9

ER -

Uniform boundary controllability and homogenization of wave equations

Abstract

Keywords

ASJC Scopus subject areas

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