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Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 163–168 (Mi tm3518)  

This article is cited in 1 scientific paper (total in 1 paper)

Equivalence of two definitions of a generalized $L_p$ solution to the initial-boundary value problem for the wave equation

V. A. Il'inab, A. A. Kuleshova

a Lomonosov Moscow State University, Moscow, Russia
b Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: In our previous papers, we introduced the notion of a generalized solution to the initial-boundary value problem for the wave equation with a boundary function $\mu(t)$ such that the integral $\int_0^T(T-t)|\mu(t)|^p dt$ exists. Here we prove that this solution is a unique solution to the problem in $L_p$ that satisfies the corresponding integral identity.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12472-ofi_m
12-01-13113-ofi-m-rzhd
12-01-31169-mol_a
Ministry of Education and Science of the Russian Federation 8209
MK-4626.2013.1
This work was supported by the Russian Foundation for Basic Research (project nos. 13-01-12472-ofi_m2, 12-01-13113-ofi-m-rzhd, and 12-01-31169-mol_a), by the Ministry of Education and Science of the Russian Federation (project no. 8209), and by a grant of the President of the Russian Federation (project no. MK-4626.2013.1).


DOI: https://doi.org/10.1134/S0371968514010105

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 155–160

Bibliographic databases:

UDC: 517.956.32+517.518.235
Received in June 2013

Citation: V. A. Il'in, A. A. Kuleshov, “Equivalence of two definitions of a generalized $L_p$ solution to the initial-boundary value problem for the wave equation”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 163–168; Proc. Steklov Inst. Math., 284 (2014), 155–160

Citation in format AMSBIB
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\by V.~A.~Il'in, A.~A.~Kuleshov
\paper Equivalence of two definitions of a~generalized $L_p$ solution to the initial-boundary value problem for the wave equation
\inbook Function spaces and related problems of analysis
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 284
\pages 163--168
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3518}
\crossref{https://doi.org/10.1134/S0371968514010105}
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\jour Proc. Steklov Inst. Math.
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\pages 155--160
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    This publication is cited in the following articles:
    1. I. S. Mokrousov, “Kriterii prinadlezhnosti klassu $W^l_p$ obobschennogo iz klassa $L_p$ resheniya volnovogo uravneniya”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:3 (2018), 297–304  mathnet  crossref  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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