Integral identity definition of a generalized solution in the class \(L_p\) to a mixed problem for the wave equation
type: Item
instance of: scholarly article
title: Integral identity definition of a generalized solution in the class \(L_p\) to a mixed problem for the wave equation
zbMATH Open document ID: 1270.35189
DOI: 10.1134/S1064562412060142
author: V. A. Il'in
author: A. A. Kuleshov
published in: Doklady Mathematics
publication date: 2013-04-03T00:00:00Z
review text: The authors show the equivalence of two definitions of generalized solutions to the initial-boundary value problem \(\partial^2_t u= \partial^2_x u\) for \((x,t)\in [0,l]\times [0,T]\), \(u= \partial_t u= 0\) for \(t=0\), \(u(0,t)= \mu(t)\), \(u(l,t)= 0\) for \(t\in [0,T]\) under the assumption that \[ \int^T_0 (T-t)|\mu(x)|^p\,dt< \infty. \]
reviewed by: Lutz Recke
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 6149528
zbMATH Keywords: equivalence of two definitions
MaRDI profile type: Publication
cites work: Solvability of mixed problems for the string oscillation equation in the space \(W_{p}^{1}\), with \(p \geq 1\)
description: scientific article; zbMATH DE number 6149528