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2021-02-25
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このアイテムへのリンクには次のURLをご利用ください:http://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
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.
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http://hdl.handle.net/11094/77680
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英語
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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