Exact controllability to the ground state solution for evolution equations of parabolic type via bilinear control

2018/11/21 by Fatiha Alabau‐Boussouira, Alabau-Boussouira, Fatiha, Piermarco Cannarsa +3 · 1 citation
Computer Science · Engineering · Mathematics · #35K90 #35Q93 #93B05 #93C10 #93C25 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1811.08806

openalex publication_date 2018/11/21 · openalex created_date 2019/10/25 · openalex updated_date 2026/07/28

Abstract

In a separable Hilbert space X, we study the linear evolution equation u'(t)+Au(t)+p(t)Bu(t)=0, where A is an accretive self-adjoint linear operator, B is a bounded linear operator on X, and p∈ L²_loc(0,+∞) is a bilinear control. We give sufficient conditions in order for the above control system to be locally controllable to the ground state solution, that is, the solution of the free equation (p≡0) starting from the ground state of A. We also derive global controllability results in large time and discuss applications to parabolic equations in low space dimension.

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