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Let us consider the wave equation $$(\partial_t^2 - \Delta)u = 0$$ on a domain $U$ with coercive homogeneous boundary conditions $$Bu|_{\partial U} = 0$$ that make $-\Delta$ self-adjoint. My question is, how can we construct such boundary conditions that the wave equation does not have finite speed of propagation any more? Can it be done at all? Thanks in advance...

Let us consider the wave equation $$(\partial_t^2 - \Delta)u = 0$$ on a domain $U$ with coercive homogeneous boundary conditions $$Bu|_{\partial U} = 0$$ My question is, how can we construct such boundary conditions that the wave equation does not have finite speed of propagation any more? Can it be done at all? Thanks in advance...

Let us consider the wave equation $$(\partial_t^2 - \Delta)u = 0$$ on a domain $U$ with coercive homogeneous boundary conditions $$Bu|_{\partial U} = 0$$ that make $-\Delta$ self-adjoint. My question is, how can we construct such boundary conditions that the wave equation does not have finite speed of propagation any more? Can it be done at all? Thanks in advance...

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Finite speed of propagation of wave equation

Let us consider the wave equation $$(\partial_t^2 - \Delta)u = 0$$ on a domain $U$ with coercive homogeneous boundary conditions $$Bu|_{\partial U} = 0$$ My question is, how can we construct such boundary conditions that the wave equation does not have finite speed of propagation any more? Can it be done at all? Thanks in advance...