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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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