Boundary controllability for a degenerate and singular wave equation

Abstract

In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in the range of both subcritical and critical potentials and for sufficiently large time, through a boundary controller acting away from the degenerate/singular point. By duality argument, we reduce the problem to an observability estimate for the corresponding adjoint system, which is proved by means of the multiplier method and new Hardy-type inequalities.

Indirect Boundary Controllability of Coupled Degenerate Wave Equations

“…Recently, several controllability results have also been obtained for scalar degenerate equations, see for example [24,25,26,27,28,29,30,31,32,33]. However, in the more complex situation of coupled degenerate hyperbolic equations, not many things are known.…”