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arXiv · 2505.09050

Taxas de decaimento dadas por fun\c{c}\~oes que variam regularmente para $C_0$-semigrupos em espa\c{c}os de Banach

Genilson Santana e Silas L. Carvalho
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Abstract

Estudamos taxas de decaimento para (possivelmente ilimitadas) semigrupos $C_0$ em espa\c{c}os de Banach sob a suposi\c{c}\~ao de que a norma do resolvente do respectivo gerador de semigrupos cresce como uma fun\c{c}\~ao vari\'avel regularmente do tipo $\beta>0$, ou seja, como $|s|^{\beta}\ell(1+|s|)$ or $|s|^{\beta}/\kappa(1+|s|)$, onde $\ell,\kappa$ s\~ao fun\c{c}\~oes arbitr\'arias e mon\'otonas e que variam lentamente. O principal resultado estende as estimativas obtidas por Deng, Rozendaal e Veraar (J. Evol. Equ. 24, 99 (2024)) para esse conjunto de fun\c{c}\~oes regularmente vari\'aveis e melhora as estimativas obtidas por Santana e Carvalho (J. Evol. Equ. 24, 28 (2024)) no caso $|s|^{\beta}\log(1+|s|)^b$, com $b\ge 0$.

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Genilson Santana e Silas L. Carvalho. 2025-05-14. Taxas de decaimento dadas por fun\c{c}\~oes que variam regularmente para $C_0$-semigrupos em espa\c{c}os de Banach. https://arxiv.org/abs/2505.09050

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