Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates

2021/12/08 by Enciso, Alberto, Shao, Arick, Vergara, Bruno
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.04457

Abstract

We consider heat operators on a convex domain Ω, with a critically singular potential that diverges as the inverse square of the distance to the boundary of Ω. We establish a general boundary controllability result for such operators in all 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 appropriate boundary conditions and the H¹-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.

Related

• Approximate boundary controllability for parabolic equations with inverse square infinite potential wells
• Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions
• Carleman estimates and controllability results for fully-discrete approximations of 1-D parabolic equations
• Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function
• Null controllability of n-dimensional parabolic equations degenerated on partial boundary