ESAIM Control Optimisation and Calculus of Variations· 2026Q1
Non null-controllability properties of the Grushin-like heat equation on 2D-manifolds
- 4citations
- Q1SCImago
- 2026year
Short summary
Achieving null-controllability for a heat equation on 2D manifolds with specific singularities requires a minimum time, especially when the control zone excludes parts of the singularity.
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Key points
- Null-controllability of a heat equation on 2D almost-Riemannian manifolds with interior singularities is studied.
- Control is achieved when the control zone does not contain the entire singularity.
- If the local metric is Grushin-like, null-controllability requires a minimal amount of time.
- The study extends to non null-controllability properties of generalized Grushin-like heat equations on Euclidean domains.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study the internal non null-controllability properties of the heat equation on 2-dimensional almost-Riemannian manifolds with an interior singularity, and under the assumption that the closure of the control zone does not contain the whole singularity. We show that if locally, around the singularity, the sub-Riemannian metric can be written in a Grushin form, or equivalently the sub-Laplacian writes as a generalized Grushin operator, then, achieving null-controllability requires at least a minimal amount of time. As locally the manifold looks like a rectangular domain, we consequently focus ourselves on the non null-controllability properties of the generalized Grushin-like heat equation on various Euclidean domains.
The authors' abstract, as published at the source. ESAIM Control Optimisation and Calculus of Variations, 2026 · DOI ↗
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Field: Control and Systems Engineering
Control and Systems EngineeringEngineering