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

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タイトル	ASYMPTOTIC CONVERGENCE OF SOLUTIONS FOR ONE-DIMENSIONAL KELLER-SEGEL EQUATIONS
著者	Iwasaki, Satoru Iwasaki, Satoru
	Osaki, Koichi Osaki, Koichi
	Yagi, Atsushi 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.
URL	http://hdl.handle.net/11094/77680
言語	英語
カテゴリ	プレプリント Preprint

著者版フラグ	author
NII資源タイプ	プレプリント
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.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/77680
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.
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	http://hdl.handle.net/11094/77680
citation_keywords	Asymptotic convergence
	Keller-Segel equations
	Chemotaxis model