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.
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
Energy conservation, Energy equipartition, Sobolev space, Sturm-Liouville problem, Wave equation
Bray, William O., and Ellen Hunter. "Wave equations & energy." AIMS Mathematics 4, no. 3 (2019): 463.