AIMS Mathematics, 2019, 4(3): 463-481. doi: 10.3934/math.2019.3.463.

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Wave equations & energy

1 Department of Mathematics, Missouri State University, 901 S. National, Springfield, MO 65897, USA
2 Department of Mathematics, Missouri State University, 901 S. National, Springfield, MO 65897, USA

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.
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Keywords wave equation; Sturm-Liouville problem; Sobolev space; energy conservation; energy equipartition

Citation: William O. Bray, Ellen Hunter. Wave equations & energy. AIMS Mathematics, 2019, 4(3): 463-481. doi: 10.3934/math.2019.3.463

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