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Optimal energy decay in a one-dimensional coupled wave–heat system

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Optimal energy decay in a one-dimensional coupled wave–heat system. / Batty, Charles; Paunonen, Lassi; Seifert, David.

In: Journal of Evolution Equations, Vol. 16, No. 3, 09.2016, p. 649–664.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Batty, C, Paunonen, L & Seifert, D 2016, 'Optimal energy decay in a one-dimensional coupled wave–heat system', Journal of Evolution Equations, vol. 16, no. 3, pp. 649–664. https://doi.org/10.1007/s00028-015-0316-0

APA

Batty, C., Paunonen, L., & Seifert, D. (2016). Optimal energy decay in a one-dimensional coupled wave–heat system. Journal of Evolution Equations, 16(3), 649–664. https://doi.org/10.1007/s00028-015-0316-0

Vancouver

Author

Batty, Charles ; Paunonen, Lassi ; Seifert, David. / Optimal energy decay in a one-dimensional coupled wave–heat system. In: Journal of Evolution Equations. 2016 ; Vol. 16, No. 3. pp. 649–664.

Bibtex - Download

@article{b2267f3348434a42aa959c38c7b90aac,
title = "Optimal energy decay in a one-dimensional coupled wave–heat system",
abstract = "We study a simple one-dimensional coupled wave–heat system and obtain a sharp estimate for the rate of energy decay of classical solutions. Our approach is based on the asymptotic theory of C0-semigroups and in particular on a result due to Borichev and Tomilov (Math Ann 347:455–478, 2010), which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the semigroup generator. This technique not only leads to an optimal result, it is also simpler than the methods used by other authors in similar situations.",
keywords = "C-semigroups, Coupled, Energy, Heat equation, Rates of decay, Resolvent estimates, Wave equation",
author = "Charles Batty and Lassi Paunonen and David Seifert",
year = "2016",
month = "9",
doi = "10.1007/s00028-015-0316-0",
language = "English",
volume = "16",
pages = "649–664",
journal = "Journal of Evolution Equations",
issn = "1424-3199",
publisher = "Springer Verlag",
number = "3",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Optimal energy decay in a one-dimensional coupled wave–heat system

AU - Batty, Charles

AU - Paunonen, Lassi

AU - Seifert, David

PY - 2016/9

Y1 - 2016/9

N2 - We study a simple one-dimensional coupled wave–heat system and obtain a sharp estimate for the rate of energy decay of classical solutions. Our approach is based on the asymptotic theory of C0-semigroups and in particular on a result due to Borichev and Tomilov (Math Ann 347:455–478, 2010), which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the semigroup generator. This technique not only leads to an optimal result, it is also simpler than the methods used by other authors in similar situations.

AB - We study a simple one-dimensional coupled wave–heat system and obtain a sharp estimate for the rate of energy decay of classical solutions. Our approach is based on the asymptotic theory of C0-semigroups and in particular on a result due to Borichev and Tomilov (Math Ann 347:455–478, 2010), which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the semigroup generator. This technique not only leads to an optimal result, it is also simpler than the methods used by other authors in similar situations.

KW - C-semigroups

KW - Coupled

KW - Energy

KW - Heat equation

KW - Rates of decay

KW - Resolvent estimates

KW - Wave equation

U2 - 10.1007/s00028-015-0316-0

DO - 10.1007/s00028-015-0316-0

M3 - Article

VL - 16

SP - 649

EP - 664

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

IS - 3

ER -