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In this article we are interested in the boundary stabilization in finitetime of one-dimensional linear hyperbolic balance laws with coefficientsdepending on time and space. We extend the so called "backstepping method" byintroducing appropriate time-dependent integral transformations in order to mapour initial system to a new one which has desired stability properties. Thekernels of the integral transformations involved are solutions to non standardmulti-dimensional hyperbolic PDEs, where the time dependence introduces severalnew difficulties in the treatment of their well-posedness. This workgeneralizes previous results of the literature, where only time-independentsystems were considered.

Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space