Abstract:The paper concerns the phenomenon of finite time stabilization in initial boundary value problems for nonautonomous decoupled linear first-order one-dimensional hyperbolic systems. We establish sufficient and necessary conditions ensuring that solutions stabilize to zero in a finite time for any initial L 2 -data. We give a combinatorial criterion stating that the stabilization occurs if and only if the matrix of reflection boundary coefficients corresponds to a directed acyclic graph. An equivalent algebraic … Show more
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