Wave equations & energy

The focus of this work is apply Fourier analytic methods based on Parseval’s equality to the computation of kinetic and potential energy of solutions of initial boundary value problems for general wave type equations on a finite interval. As a consequence, an energy equipartion principle for the sol...

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Bibliographic Details
Published inAIMS mathematics Vol. 4; no. 3; pp. 463 - 481
Main Authors O. Bray, William, Hunter, Ellen
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2019
Subjects
energy conservation
energy equipartition
Sobolev space
Sturm-Liouville problem
wave equation
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Summary:The focus of this work is apply Fourier analytic methods based on Parseval’s equality to the computation of kinetic and potential energy of solutions of initial boundary value problems for general wave type equations on a finite interval. As a consequence, an energy equipartion principle for the solution is obtained. Within our methods are some new results regarding eigenfunction expansions arising from regular Sturm-Liouville problems in Sobolev spaces.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2019.3.463