The Dirichlet problem for telegraph equation in a rectangular domain

Yu. K. Sabitova

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 46-56.

Résumé

We investigate the Dirichlet problem for telegraph equation in rectangular domain. We establish a criterion of uniqueness. The solution to the problem is constructed in the form of the sum of orthogonal series. In substantiation of convergence of the series there appears the problem of small denominators. In connection with this we establish the estimates of separation from zero of denominators with the corresponding asymptotics which allow to substantiate the existence of a regular solution and prove its stability depending on boundary functions.

Détail

Keywords: telegraph equation, the Dirichlet problem, spectral method, criterion of uniqueness, small denominators, stability.

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