ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR THE LAPLACE EQUATION WITH A LARGE SPECTRAL PARAMETER AND THE INHOMOGENEOUS ROBIN TYPE CONDITIONS

Ikehata, Masaru; Kawashita, Mishio

doi:info:doi/10.18910/67751

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タイトル	ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR THE LAPLACE EQUATION WITH A LARGE SPECTRAL PARAMETER AND THE INHOMOGENEOUS ROBIN TYPE CONDITIONS
著者	Ikehata, Masaru Ikehata, Masaru
著者	Kawashita, Mishio Kawashita, Mishio
抄録	Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this paper, asymptotic behavior of the solutions of the reduced problem for the classical heat equation in bounded domains with the inhomogeneous Robin type conditions is discussed. The boundary of the domain consists of two disjoint surfaces, outside one and inside one. When there are inhomogeneous Robin type data at both boundaries, it is shown that asymptotics of the value of the solution with respect to the large parameter at a given point inside the domain is closely connected to the distance from the point to the both boundaries. It is also shown that if the inside boundary is strictly convex and the data therein vanish, then the asymptotics is different from the previous one. The method for the proof employs a representation of the solution via single layer potentials. It is based on some non trivial estimates on the integral kernels of related integral equations which are previously established and used in studying an inverse problem for the heat equation via the enclosure method.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	55
号	1
開始ページ	117
終了ページ	163
刊行年月	2018-01
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/67751
言語	英語
DOI	info:doi/10.18910/67751
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 55, Number 1 （2018-1）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.55(1) P.117-P.163
DC.title	ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR THE LAPLACE EQUATION WITH A LARGE SPECTRAL PARAMETER AND THE INHOMOGENEOUS ROBIN TYPE CONDITIONS
DC.creator	Ikehata, Masaru
DC.creator	Kawashita, Mishio
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2018-01
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/67751
DCTERMS.abstract	Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this paper, asymptotic behavior of the solutions of the reduced problem for the classical heat equation in bounded domains with the inhomogeneous Robin type conditions is discussed. The boundary of the domain consists of two disjoint surfaces, outside one and inside one. When there are inhomogeneous Robin type data at both boundaries, it is shown that asymptotics of the value of the solution with respect to the large parameter at a given point inside the domain is closely connected to the distance from the point to the both boundaries. It is also shown that if the inside boundary is strictly convex and the data therein vanish, then the asymptotics is different from the previous one. The method for the proof employs a representation of the solution via single layer potentials. It is based on some non trivial estimates on the integral kernels of related integral equations which are previously established and used in studying an inverse problem for the heat equation via the enclosure method.
DC.identifier	info:doi/10.18910/67751
citation_title	ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR THE LAPLACE EQUATION WITH A LARGE SPECTRAL PARAMETER AND THE INHOMOGENEOUS ROBIN TYPE CONDITIONS
citation_author	Ikehata, Masaru
citation_author	Kawashita, Mishio
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2018-01
citation_journal_title	Osaka Journal of Mathematics
citation_volume	55
citation_issue	1
citation_firstpage	117
citation_lastpage	163
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/67751
citation_doi	info:doi/10.18910/67751

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