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A backward uniqueness result for the wave equation with absorbing boundary conditions. (English) Zbl 1337.47111
Summary: We consider the wave equation $$u_{tt}=\Delta u$$ on a bounded domain $$\Omega\subset{\mathbb R}^n$$, $$n>1$$, with smooth boundary of positive mean curvature. On the boundary, we impose the absorbing boundary condition $${\partial u\over\partial\nu}+u_t=0$$. We prove uniqueness of solutions backward in time.

##### MSC:
 47N20 Applications of operator theory to differential and integral equations 35L05 Wave equation 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 47D06 One-parameter semigroups and linear evolution equations
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##### References:
 [1] G. Avalos, Backward uniqueness for a PDE fluid-structure interaction,, preprint [2] G. Avalos, Backward uniqueness of the s.c. semigroup arising in parabolic-hyperbolic fluid-structure interaction,, J. Diff. Eq., 245, 737, (2008) · Zbl 1158.35300 [3] G. Avalos, Backwards uniqueness of the $$C_0$$-semigroup associated with a parabolic-hyperbolic Stokes-Lamé partial differential equation system,, Trans. Amer. Math. Soc., 362, 3535, (2010) · Zbl 1204.35011 [4] I. Lasiecka, Backward uniqueness for thermoelastic plates with rotational forces,, Semigroup Forum, 62, 217, (2001) · Zbl 1015.74030 [5] M. Renardy, Backward uniqueness for linearized compressible flow,, Evol. Eqns. Control Th., 4, 107, (2015) · Zbl 1338.47046
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