ASYMPTOTIC CONVERGENCE OF SOLUTIONS FOR ONE-DIMENSIONAL KELLER-SEGEL EQUATIONS

Iwasaki, Satoru; Osaki, Koichi; Yagi, Atsushi

アクセス数:505件（2025-07-01 17:15 集計）

固定URL: https://hdl.handle.net/11094/77680

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タイトル	ASYMPTOTIC CONVERGENCE OF SOLUTIONS FOR ONE-DIMENSIONAL KELLER-SEGEL EQUATIONS
著者	NRID 1000000845604 1000000845604 ORCID 0000-0002-3719-4705 0000-0002-3719-4705 researchmap permalink s_iwasaki s_iwasaki Scopus Author ID 57193648564 57193648564 著者名 Iwasaki, Satoru
	NRID 1000040353320 1000040353320 著者名 Osaki, Koichi
	NRID 1000070116119 1000070116119 著者名 Yagi, Atsushi
キーワード等	Asymptotic convergence
	Keller-Segel equations
	Chemotaxis model
抄録	The second and third authors of this paper have constructed in [14] finite-dimensional attractors for the one-dimensional Keller-Segel equations. They have also remarked in [14, Section 7] that, when the sensitivity function is a linear function, the equations admit a global Lyapunov function. But at that moment they could not show the asymptotic convergence of solutions. This paper is then devoted to supplementing the results of [14, Section 7] by showing that, as t → ∞, every solution necessarily converges to a stationary solution by using the Lojasiewicz-Simon gradient inequality of the Lyapunov function.
言語	英語
ハンドルURL	https://hdl.handle.net/11094/77680
アクセス権	open access
出版タイプ	Author’s Original

資源タイプ	その他
ローカル資源タイプ	プレプリント
DCMI資源タイプ	text
DC.title	ASYMPTOTIC CONVERGENCE OF SOLUTIONS FOR ONE-DIMENSIONAL KELLER-SEGEL EQUATIONS
DC.creator	Iwasaki, Satoru
	Osaki, Koichi
	Yagi, Atsushi
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DC.subject	Asymptotic convergence
	Keller-Segel equations
	Chemotaxis model
DCTERMS.abstract	The second and third authors of this paper have constructed in [14] finite-dimensional attractors for the one-dimensional Keller-Segel equations. They have also remarked in [14, Section 7] that, when the sensitivity function is a linear function, the equations admit a global Lyapunov function. But at that moment they could not show the asymptotic convergence of solutions. This paper is then devoted to supplementing the results of [14, Section 7] by showing that, as t → ∞, every solution necessarily converges to a stationary solution by using the Lojasiewicz-Simon gradient inequality of the Lyapunov function.
DC.format	77680
citation_title	ASYMPTOTIC CONVERGENCE OF SOLUTIONS FOR ONE-DIMENSIONAL KELLER-SEGEL EQUATIONS
citation_author	Iwasaki, Satoru
	Osaki, Koichi
	Yagi, Atsushi
citation_language	英語
citation_public_url	https://hdl.handle.net/11094/77680