Exact boundary controllability of 1-D parabolic and hyperbolic degenerate equations. (English) Zbl 1327.35211
In this paper, the authors study the boundary controllability of a class of one-dimensional degenerate equations. The novelty of this work is that the control acts through the part of the boundary where degeneration occurs. First, the authors consider a class of degenerate hyperbolic equations. Then, they 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.
Reviewer: Yuanyuan Ke (Beijing)
MSC:
35K65 | Degenerate parabolic equations |
35L80 | Degenerate hyperbolic equations |
93B05 | Controllability |
93B07 | Observability |