Boundary controllability for a one-dimensional heat equation with a\n singular inverse-square potential

2015/09/17 by Umberto Biccari, Biccari, Umberto
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1509.05178

openalex publication_date 2015/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze controllability properties for the one-dimensional heat equation\nwith singular inverse-square potential u_t-u_xx-
frac
mux²u=0,
;
;
;\n(x,t)
in(0,1)
times(0,T). For any \μ<1/4, we prove that the equation is\nnull controllable through a boundary control f\∈ H¹(0,T) acting at the\nsingularity point x=0. This result is obtained employing the moment method by\nFattorini and Russell.\n

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