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Exact solution to a multidimensional wave equation with delay

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  • Jornet, Marc

Abstract

This paper deals with a mixed problem for the wave equation with discrete delay τ>0,utt(t,x)=a12Δxu(t,x)+a22Δxu(t−τ,x)+b1u(t,x)+b2u(t−τ,x),t>τ,0≤x≤l,with Dirichlet boundary conditions. The exact infinite series solution is constructed by the method of separation of variables, where the time-dependent functions of the decomposition satisfy second-order delay differential equations. Our approach is based on and extends the work by Rodríguez, Roales and Martín (Applied Mathematics and Computation, 2012).

Suggested Citation

  • Jornet, Marc, 2021. "Exact solution to a multidimensional wave equation with delay," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321005105
    DOI: 10.1016/j.amc.2021.126421
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    References listed on IDEAS

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    1. Joseph Wiener & Lokenath Debnath, 1992. "A wave equation with discontinuous time delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-8, January.
    2. M. A. Castro & F. Rodríguez & J. Escolano & J. A. Martín, 2013. "Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, December.
    3. Joseph Wiener & Lokenath Debnath, 1997. "Boundary value problems for the diffusion equation with piecewise continuous time delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-9, January.
    4. Josef Diblík & Denis Khusainov & Oleksandra Kukharenko & Zdeněk Svoboda, 2012. "Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-27, July.
    5. García, M.A. & Castro, M.A. & Martín, J.A. & Rodríguez, F., 2018. "Exact and nonstandard numerical schemes for linear delay differential models," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 337-345.
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    Cited by:

    1. Kerr, Gilbert & González-Parra, Gilberto, 2022. "Accuracy of the Laplace transform method for linear neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 308-326.

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