In this article we are interested in the boundary stabilization in finite
time of one-dimensional linear hyperbolic balance laws with coefficients
depending on time and space. We extend the so called "backstepping method" by
introducing appropriate time-dependent integral transformations in order to map
our initial system to a new one which has desired stability properties. The
kernels of the integral transformations involved are solutions to non standard
multi-dimensional hyperbolic PDEs, where the time dependence introduces several
new difficulties in the treatment of their well-posedness. This work
generalizes previous results of the literature, where only time-independent
systems were considered
