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The Neumann problem for nonstationary systems in tubular domains. (English. Russian original) Zbl 0898.35020
Math. Notes 60, No. 4, 475-478 (1996); translation from Mat. Zametki 60, No. 4, 631-634 (1996).
We consider the system $(-1)^{m-1} \left[\sum^m_{| p|,| q|=1} D^p \bigl(a_{pq} (x,t)D^q u\bigr) +\sum^m_{| p|=1} a_p(x,t) D^pu+ a(x,t)u \right]- u_{tt} =f,$ where $$(-1)^{| p| +| q|} \overline a_{pq} =a_{qp}$$, $$a_p$$, and $$a$$ are bounded measurable complex-valued $$r\times r$$ matrices on the tubular domain $$Q_T= \{(x,t): x\in \Omega$$, $$t\in [0,T]\}$$, and $$\Omega \subset \mathbb{R}^n$$ is a bounded domain whose boundary satisfies the Lipschitz condition. We prove smoothness with respect to time of generalized solutions.
##### MSC:
 35D05 Existence of generalized solutions of PDE (MSC2000) 35L55 Higher-order hyperbolic systems 35L20 Initial-boundary value problems for second-order hyperbolic equations 74B05 Classical linear elasticity
##### Keywords:
smoothness with respect to time
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##### References:
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