Arick Shao (Queen Mary, University of London)
Control of parabolic equations with inverse square infinite potential wells
Abstract:
We consider heat operators on a bounded convex domain, with a critically sin-
gular potential diverging as the inverse square of the distance to the boundary
of the domain. We establish a general boundary controllability result for such
operators in all spatial dimensions, in particular providing the first such result
in more than one spatial dimension. The key step in the proof is a novel global
Carleman estimate that captures both the relevant boundary asymptotics and
the appropriate energy for this problem. The estimate is derived by combining
two intermediate Carleman inequalities with distinct and carefully constructed
weights involving non-smooth powers of the boundary distance.
This is joint work
with Alberto Enciso (ICMAT) and Bruno Vergara (Brown).