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

DOI10.1134/S0081543814010106zbMath1307.35157MaRDI QIDQ483386

A. A. Kuleshov, Vladimir Il'in

Publication date: 17 December 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

one space dimension

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (4)

On a mixed problem for Hilfer type fractional differential equation with degeneration ⋮ The problem of two-dimensional string vibrations with a nonlinear condition ⋮ Formula of Kirchhoff type for mixed problem ⋮ Criterion for a Generalized Solution in the Class Lp for the Wave Equation to Be in the Class W1 p

Cites Work

• Solvability of mixed problems for the string oscillation equation in the space \(W_{p}^{1}\), with \(p \geq 1\)
• Necessary and sufficient conditions for a generalized solution to the initial-boundary value problem for the wave equation to belong to \(W_p^1\) with \(p\geq 1\)

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