Periodic damping gives polynomial energy decay

Jared Wunsch

doi:10.4310/MRL.2017.v24.n2.a15

Periodic damping gives polynomial energy decay

Jared Wunsch^*

^*Corresponding author for this work

Mathematics

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

6 Scopus citations

Abstract

Let u solve the damped Klein.Gordon equation ( ∂^Ý _t-σ +∂^Ý _xj + mId+(x)∂_t u = 0 on Rn with m > 0 and Á . 0 bounded below on a 2ÎZn-invariant open set by a positive constant. We show that the energy of a solution decays at a polynomial rate. This is proved via a periodic observability estimate on Rn.

Original language	English (US)
Pages (from-to)	571-580
Number of pages	10
Journal	Mathematical Research Letters
Volume	24
Issue number	2
DOIs	https://doi.org/10.4310/MRL.2017.v24.n2.a15
State	Published - 2017

ASJC Scopus subject areas

Mathematics(all)

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10.4310/MRL.2017.v24.n2.a15

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title = "Periodic damping gives polynomial energy decay",

abstract = "Let u solve the damped Klein.Gordon equation ( ∂{\'Y} t-σ +∂{\'Y} xj + mId+(x)∂t u = 0 on Rn with m > 0 and {\'A} . 0 bounded below on a 2{\^I}Zn-invariant open set by a positive constant. We show that the energy of a solution decays at a polynomial rate. This is proved via a periodic observability estimate on Rn.",

author = "Jared Wunsch",

year = "2017",

doi = "10.4310/MRL.2017.v24.n2.a15",

language = "English (US)",

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T1 - Periodic damping gives polynomial energy decay

AU - Wunsch, Jared

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N2 - Let u solve the damped Klein.Gordon equation ( ∂Ý t-σ +∂Ý xj + mId+(x)∂t u = 0 on Rn with m > 0 and Á . 0 bounded below on a 2ÎZn-invariant open set by a positive constant. We show that the energy of a solution decays at a polynomial rate. This is proved via a periodic observability estimate on Rn.

AB - Let u solve the damped Klein.Gordon equation ( ∂Ý t-σ +∂Ý xj + mId+(x)∂t u = 0 on Rn with m > 0 and Á . 0 bounded below on a 2ÎZn-invariant open set by a positive constant. We show that the energy of a solution decays at a polynomial rate. This is proved via a periodic observability estimate on Rn.

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U2 - 10.4310/MRL.2017.v24.n2.a15

DO - 10.4310/MRL.2017.v24.n2.a15

M3 - Article

AN - SCOPUS:85025647378

SN - 1073-2780

VL - 24

SP - 571

EP - 580

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 2

ER -

Periodic damping gives polynomial energy decay

Abstract

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