@article{8665918,
  abstract     = {{In this article we propose a new formulation of boundary-value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary. We prove the well-posedness of boundary-value problem in the classical and generalized senses. To substantiate the well-posedness of this problem it is necessary to have an effective representation of the general solution of the problem. In this direction we obtain a convenient representation of the general solution for the wave equation in a rectangular domain based on d'Alembert classical formula. The constructed general solution automatically satisfies the boundary conditions by a spatial variable. Further, by setting different boundary conditions according to temporary variable, we get some functional or functional-differential equations. Thus, the proof of the well-posedness of the formulated problem is reduced to question of the existence and uniqueness of solutions of the corresponding functional equations.}},
  articleno    = {{281}},
  author       = {{Sadybekov, Makhmud and Yessirkegenov, Nurgissa}},
  issn         = {{1072-6691}},
  journal      = {{ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS}},
  keywords     = {{Wave equation,well-posedness of problems,classical solution,strong solution,d'Alembert's formula}},
  language     = {{eng}},
  pages        = {{9}},
  title        = {{Boundary-value problems for wave equations with data on the whole boundary}},
  volume       = {{2016}},
  year         = {{2016}},
}

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