Generalized solutions of the wave equation in the classes \(L _{p }\) and \(W^{1}_{p}\) with \( p \geq 1\)

DOI10.1134/S106456241205016XzbMath1393.35124MaRDI QIDQ1930829

A. A. Kuleshov, Vladimir Il'in

Publication date: 14 January 2013

Published in: Doklady Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Wave equation (35L05) Weak solutions to PDEs (35D30)

Related Items (3)

Transformation operators in controllability problems for the wave equations with variable coefficients on a half-axis controlled by the Dirichlet boundary condition ⋮ Solvability of mixed problems for the Klein-Gordon-Fock equation in the class \(L_p\) for \(p\geq1\) ⋮ 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 \(p \geq 1\)
• Boundary control of oscillations at one endpoint with the other endpoint fixed in terms of a finite-energy generalized solution of the wave equation

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