Geodesic
Inverse problems for initial conditions of the mixed problem for the telegraph equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 111-133 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we examine inverse problems for initial conditions for the wave and telegraph equations and state uniqueness criteria. Solutions of these problems are constructed in the series form. In the proof of uniform convergence of these series, the problem on small denominators appear. We prove estimates of small denominators separated from zero and obtain asymptotics that allow one to justify the convergence in the class of regular solutions.
Keywords: telegraph equation, inverse problem, Dirichlet problem, mixed boundary conditions, uniqueness criteria, series, small denominators.
Mots-clés : existence 
@article{INTO_2017_141_a9,
     author = {K. B. Sabitov and A. R. Zaynullov},
     title = {Inverse problems for initial conditions of the mixed problem for the telegraph equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {111--133},
     year = {2017},
     volume = {141},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_141_a9/}
}
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K. B. Sabitov; A. R. Zaynullov. Inverse problems for initial conditions of the mixed problem for the telegraph equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 111-133. http://geodesic.mathdoc.fr/item/INTO_2017_141_a9/