Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density
Abstract
We prove observability and nullcontrollability 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 $S \neq \{0\}$ 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 DOI:
 10.48550/arXiv.2201.02370
 arXiv:
 arXiv:2201.02370
 Bibcode:
 2022arXiv220102370D
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Optimization and Control;
 Primary 35B99;
 Secondary 35Q70;
 35Pxx;
 93Bxx
 EPrint:
 30 pages