Differential Equations

, Volume 55, Issue 2, pp 270–273 | Cite as

Generalized d’Alembert Formula for the Wave Equation with Discontinuous Coefficients

  • D. S. AnikonovEmail author
  • D. S. Konovalova
Short Communications


We consider a second-order differential equation that is a mathematical model of transverse vibrations of a string or longitudinal vibrations of an elastic rod. The coefficients of the second derivatives are piecewise constant functions. An existence and uniqueness theorem is proved and an explicit formula is given for the generalized solution of the Cauchy problem.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.Sobolev Institute of MathematicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia

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