Solvability of mixed problems for the string oscillation equation in the space \(W_{p}^{1}\), with \(p \geq 1\)
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Publication:416875
DOI10.1134/S1064562411070192zbMath1247.35067MaRDI QIDQ416875
A. A. Kholomeeva, E. I. Moiseev
Publication date: 10 May 2012
Published in: Doklady Mathematics (Search for Journal in Brave)
Initial-boundary value problems for second-order hyperbolic equations (35L20) Wave equation (35L05) Strings (74K05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Related Items
Generalized solutions of the wave equation in the classes \(L _{p }\) and \(W^{1}_{p}\) with \( p \geq 1\), Solvability of the mixed problem for the wave equation with a dynamic boundary condition, On some properties of generalized solutions of the wave equation in the classes \(L _{p }\) and \(W^1_p\) for \(p \geq 1\), Integral identity definition of a generalized solution in the class \(L_p\) to a mixed problem for the wave equation, Equivalence of two definitions of a generalized \(L_p\) solution to the initial-boundary value problem for the wave equation, Optimization of the boundary control of string vibrations at one string end with a given mode at the other end, 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
- Optimal boundary control by an elastic force at one end and a displacement at the other end for an arbitrary sufficiently large time interval in the string vibration problem
- Optimization of boundary controls by displacements at two ends of a string for an arbitrary sufficiently large time interval
- Optimal boundary displacement control of string vibrations with a nonlocal oddness condition of the first kind
- Optimization of boundary controls of string vibrations
