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On solution of the mixed boundary value problem for the string equation. (Russian) Zbl 0745.35025

The author proves unique solvability for the problem \[ \partial^ 2u/\partial t^ 2=\partial^ 2u/\partial x^ 2-p(t,x)\quad (0<t<T,\;0<x<L), \]
\[ u(t,0)=u(t,L)=0\quad (0<t<T), \]
\[ u(0,x)=\varphi(x),\quad {\partial u\over\partial t}(0,x)=\psi(x) \quad (0<x<L) \] for smooth data \(\varphi\) and \(\psi\).

MSC:

35M10 PDEs of mixed type
35L05 Wave equation
35R25 Ill-posed problems for PDEs
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