Null-controllability and control cost estimates for the heat equation on\n unbounded and large bounded domains

2018/10/26 by Michela Egidi, Egidi, Michela, Ivica Nakić +9 · 1 citation
Engineering · Mathematics · #35K05 #35Q93 #35R15 #93B05 #93C20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1810.11229

openalex publication_date 2018/10/26 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

We survey recent results on the control problem for the heat equation on\nunbounded and large bounded domains. First we formulate new uncertainty\nrelations, respectively spectral inequalities. Then we present an abstract\ncontrol cost estimate which improves upon earlier results. It is particularly\ninteresting when combined with the earlier mentioned spectral inequalities\nsince it yields sharp control cost bounds in several asymptotic regimes. We\nalso show that control problems on unbounded domains can be approximated by\ncorresponding problems on a sequence of bounded domains forming an exhaustion.\nOur results apply also for the generalized heat equation associated with a\nSchr "odinger semigroup.\n

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