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

Abstract

International audienceIn 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