Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density

Abstract

We prove observability and null-controllability for quadratic parabolic differential equations. The sensor set is allowed to be sparse and have finite volume if the generator has trivial singular space $S$. In the case of generators with singular space $S\ne \{0\}$ the sensor set is permitted to decay in directions determined by $S$. The proof is based on dissipation estimates for the quadratic differential operator with respect to spectral projections of partial harmonic oscillators and corresponding uncertainty relations.

30 pages; some typos fixed and minor editorial changes

References in corpus (3)

• An abstract Logvinenko-Sereda type theorem for spectral subspaces
• Uncertainty principle for Hermite functions and null-controllability with sensor sets of decaying density
• The Laplacian on Cartesian products with mixed boundary conditions

Cited by in corpus (3)

• Uncertainty principles with error term in Gelfand-Shilov spaces
• Unique continuation estimates for Baouendi--Grushin equations on cylinders
• Sturm-Liouville Problems And Global Bounds By Small Control Sets And applications to quantum graphs