Null-controllability of the Generalized Baouendi-Grushin heat like equations

2023/10/17 by Philippe Jaming, Jaming, Philippe, Yunlei Wang +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2310.11215

openalex publication_date 2023/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove null-controllability results for the heat equation associated tofractional Baouendi-Grushin operators ∂_t u+(-Δ_x-V(x)Δ_y)^s u= \mathbb1_Ωh where V is a potential that satisfies some power growth conditions and the set Ωis thick in some sense. This extends previously known results for potentials V(x)=|x|^2k.To do so, we study Zhu-Zhuge's spectral inequality for Schrödinger operators with power growth potentials, and give a precised quantitative form of it.

Citations

• Null-controllability of evolution equations associated with fractional Shubin operators through quantitative Agmon estimates
• SPECTRAL INEQUALITIES FOR ANISOTROPIC SHUBIN OPERATORS
• Null-controllability properties of the generalized two-dimensional Baouendi-Grushin equation with non-rectangular control sets
• Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability
• Spectral inequality for Schrödinger equations with power growth potentials

Related

• Null-controllability properties of the generalized two-dimensional Baouendi-Grushin equation with non-rectangular control sets
• Quantitative 2D propagation of smallness and control for 1D heat equations with power growth potentials
• Unique continuation estimates for Baouendi--Grushin equations on cylinders
• Observability of Baouendi-Grushin-Type Equations Through Resolvent Estimates
• Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability