Research article

Wave equations & energy

  • Received: 01 February 2019 Accepted: 29 April 2019 Published: 10 May 2019
  • MSC : 35L05, 34B24

  • 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.

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

    Related Papers:

  • 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.


    加载中


    [1] S. E. H. Miri, Fractional power function spaces associated to regular Sturm-Liouville problems, Electronic Journal of Differential Equations (EJDE)[electronic only], 2005.
    [2] A. S. Bescovitch, Almost Periodic Functions, Dover Publications, 1959.
    [3] H. Bohr, Almost Periodic Functions, Chelsea, 1951.
    [4] A. R. Brodsky, On the asymptotic behaviour of solutions of wave equations, Proc. Amer. Math. Soc., 18 (1967), 207-208. doi: 10.1090/S0002-9939-1967-0212417-X
    [5] W. O. Bray, A Journey into Partial Differential Equations, Jones & Bartlett Learning, 2012.
    [6] G. Birkhoff, G. Carlo-Rota, Ordinary Differential Equations, 4th edition, J. Wiley, 1989.
    [7] C. T. Fulton, S. A. Pruess, Eigenvalue and eigenfunction asypmtotics for regular Sturm-Liouville problems, Journal of Mathematical Analysis Applications, 188 (1994), 297-340. doi: 10.1006/jmaa.1994.1429
    [8] J. A. Goldstein, An asymptotic property of solutions of wave equations, Proceedings of the American Mathematical Society, 23 (1969), 359-363. doi: 10.1090/S0002-9939-1969-0250125-1
    [9] G. Leoni, A First Course in Sobolev Spaces, Vol. 105, American Mathematical Soc., 2009.
    [10] R. L. Wheeden, Measure and Integral, An Introduction to Real Analysis, 2 ed., CRC Press, 2015.
  • Reader Comments
  • © 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3143) PDF downloads(576) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog