关于时间尺度上的 C 0 半群和热动力方程的近似可控性的定理

Pub Date : 2024-05-06 DOI:10.2989/16073606.2024.2345845

Martin Bohner, C. Duque, Hugo Leiva, Zoraida Sívoli

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引用次数: 0

摘要

.在本文中，我们提出了一种 Lemma，它使我们能够描述一大类时间尺度上的 C 0 -semigroups 的特征，并可将其应用于证明时域为时间尺度的偏微分方程系统解的存在性和唯一性。所得到的结果被应用于研究热方程在时间尺度上的可控性。本文提出的 Lemma 可以看作是 H. Leiva 在 [28] 中针对 [0 , ∞ ) 中的半群所证明的 Lemma 的统一。

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

. 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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