Research Article

A lemma on C ₀-semigroups on time scales and approximate controllability of the heat dynamic equation

Published in: Quaestiones Mathematicae
Volume 47 , issue 9 , 2024 , pages: 1807–1826

DOI: 10.2989/16073606.2024.2345845

Author(s): Martin Bohner Missouri University of Science and Technology, USA , Cosme Duque Universidad de Los Andes, , Hugo Leiva University YachayTech, School of Mathematical and Computational Sciences, Ecuador , Zoraida Sivoli Universidad Siglo 21,

Keywords: Primary: 34N05 , 47D06 , Secondary: 35K90 , 93C20 , Time scales , C ₀-semigroups , infinitesimal generator , heat equation , controllability

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Abstract

In this paper, we present a lemma that allows us to characterize a broad class of C ₀-semigroups on time scales, which can be applied to prove existence and uniqueness of solutions of systems of partial differential equations where the time domain is a time scale. The result obtained is applied to study the controllability of the heat equation on time scales. The lemma presented in this paper can be seen as a unification of the one proved by H. Leiva in [28], for semigroups in [0,∞).

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