On a generalization of the initial-boundary problem for the vibrating string equation

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Amanov D., Ibragimov G., Kili�man A.

Symmetry, vol.11, no.1, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.3390/sym11010073
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Initial conditions, Regular solution, Spectral decomposition, The existence of a solution, The uniqueness of the solution, Vibrating string equation
  • Istanbul Gelisim University Affiliated: No

Abstract

© 2019 by the authors.In the present paper, we study a generalization of the initial-boundary problem for the inhomogeneous vibrating string equation. The initial conditions include the higher order derivatives of the unknown function. The problem is studied under homogeneous boundary conditions of the first kind. The uniqueness and existence of a regular solution of the problem are proved. To prove the main result we use the spectral decomposition method.