Lyapunov functions for dynamically gradient impulsive systems

Autor(es)

Bonotto, Everaldo M. ; Bortolan, Matheus C. ; Pereira, Fabiano

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 384, p. 47-pg., 2023-12-18.

Resumo

In this paper, we present a comprehensive theory of generalized gradient and dynamically gradient impulsive semigroups. Our work establishes the equivalence of these classes, relative to a separated family of isolated invariant sets, similar to the non-impulsive case. However, the presence of impulses poses certain challenges, which we overcome by considering a slightly modified notion of attraction. Additionally, we provide an illustration of the theory by demonstrating that a reaction-diffusion equation-driven impulsive semigroup possesses a Lyapunov function. (c) 2023 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 20/14075-6 - Sistemas dinâmicos e seus atratores sob perturbação
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Temático