EXACT BOUNDARY CONTROLLABILITY OF 1-D PARABOLIC AND HYPERBOLIC DEGENERATE EQUATIONS?

摘要

The boundary controllability of a class of one-dimensional degenerate equations is studied in this paper. The novelty of this work is that the control acts through the part of the boundary where degeneracy occurs. First we consider a class of degenerate hyperbolic equations. Then, we prove sharp observability estimates for these equations using nonharmonic Fourier series. The transmutation method yields a result for the corresponding class of degenerate parabolic equations.