Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights

This paper deals with the abstract evolution equations in Ls{L}^{s}-spaces with critical temporal weights. First, embedding and interpolation properties of the critical Ls{L}^{s}-spaces with different exponents ss are investigated, then solvability of the linear evolution equation, attached to which...

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Autores principales:	Zhang Qinghua, Tan Zhizhong
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	critical l s-space sectorial operator maximal regularity evolution equation solvability 34k30 47d06 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a3fdb309a14e4b5ca405757050257d41
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spelling	oai:doaj.org-article:a3fdb309a14e4b5ca405757050257d412021-12-05T14:10:52ZSolvability of the abstract evolution equations in Ls-spaces with critical temporal weights2391-545510.1515/math-2021-0027https://doaj.org/article/a3fdb309a14e4b5ca405757050257d412021-04-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0027https://doaj.org/toc/2391-5455This paper deals with the abstract evolution equations in Ls{L}^{s}-spaces with critical temporal weights. First, embedding and interpolation properties of the critical Ls{L}^{s}-spaces with different exponents ss are investigated, then solvability of the linear evolution equation, attached to which the inhomogeneous term ff and its average Φf\Phi f both lie in an L1/ss{L}_{1\hspace{-0.08em}\text{/}\hspace{-0.08em}s}^{s}-space, is established. Based on these results, Cauchy problem of the semi-linear evolution equation is treated, where the nonlinear operator F(t,u)F\left(t,u) has a growth number ρ≥s+1\rho \ge s+1, and its asymptotic behavior acts like α(t)/t\alpha \left(t)\hspace{-0.1em}\text{/}\hspace{-0.1em}t as t→0t\to 0 for some bounded function α(t)\alpha \left(t) like (−logt)−p{\left(-\log t)}^{-p} with 2≤p<∞2\le p\lt \infty .Zhang QinghuaTan ZhizhongDe Gruyterarticlecritical l s-spacesectorial operatormaximal regularityevolution equationsolvability34k3047d06MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 111-120 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	critical l s-space sectorial operator maximal regularity evolution equation solvability 34k30 47d06 Mathematics QA1-939
spellingShingle	critical l s-space sectorial operator maximal regularity evolution equation solvability 34k30 47d06 Mathematics QA1-939 Zhang Qinghua Tan Zhizhong Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
description	This paper deals with the abstract evolution equations in Ls{L}^{s}-spaces with critical temporal weights. First, embedding and interpolation properties of the critical Ls{L}^{s}-spaces with different exponents ss are investigated, then solvability of the linear evolution equation, attached to which the inhomogeneous term ff and its average Φf\Phi f both lie in an L1/ss{L}_{1\hspace{-0.08em}\text{/}\hspace{-0.08em}s}^{s}-space, is established. Based on these results, Cauchy problem of the semi-linear evolution equation is treated, where the nonlinear operator F(t,u)F\left(t,u) has a growth number ρ≥s+1\rho \ge s+1, and its asymptotic behavior acts like α(t)/t\alpha \left(t)\hspace{-0.1em}\text{/}\hspace{-0.1em}t as t→0t\to 0 for some bounded function α(t)\alpha \left(t) like (−logt)−p{\left(-\log t)}^{-p} with 2≤p<∞2\le p\lt \infty .
format	article
author	Zhang Qinghua Tan Zhizhong
author_facet	Zhang Qinghua Tan Zhizhong
author_sort	Zhang Qinghua
title	Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
title_short	Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
title_full	Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
title_fullStr	Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
title_full_unstemmed	Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
title_sort	solvability of the abstract evolution equations in ls-spaces with critical temporal weights
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/a3fdb309a14e4b5ca405757050257d41
work_keys_str_mv	AT zhangqinghua solvabilityoftheabstractevolutionequationsinlsspaceswithcriticaltemporalweights AT tanzhizhong solvabilityoftheabstractevolutionequationsinlsspaceswithcriticaltemporalweights
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Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights

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