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arXiv · 2201.02370

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

Alexander Dicke·Albrecht Seelmann·Ivan Veselic
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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 $S \neq \{0\}$ 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.

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Alexander Dicke, Albrecht Seelmann, Ivan Veselic. 2022-01-07. Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density. https://doi.org/10.1051/cocv%2F2023063

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