Representation formulas of the solutions to the Cauchy problems for first order systems

Tajiri, Masaki; Umeda, Tomio

doi:info:doi/10.18910/4372

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タイトル	Representation formulas of the solutions to the Cauchy problems for first order systems
著者	Tajiri, Masaki Tajiri, Masaki
著者	Umeda, Tomio Umeda, Tomio
抄録	Representation formulas of the solutions to the Cauchy problems for first order systems of the forms ∂u/∂t - Σ_(j=1)^(d)A_j(t)∂u/∂x_j - A_0(t)u = f are established. The coefficients A_j's are assumed to be matrix-valued functions of the forms A_j(t) = α_j(t)I +β_j(t)M_j, where α_j (t),β_j(t), j = 1,...,d, are real-valued continuous functions, the eigenvalues of the matrices M_j, j = 1,...,d, are real, and the commutators [M_j, M_l] = 0 for all j, l = 0, 1,...,d. No restrictions on the multiplicities of the characteristic roots are imposed.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	44
号	1
開始ページ	197
終了ページ	205
刊行年月	2007-03
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/4372
言語	英語
DOI	info:doi/10.18910/4372

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
日付	2007-03
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.44(1) P.197-P.205
DC.title	Representation formulas of the solutions to the Cauchy problems for first order systems
DC.creator	Tajiri, Masaki
DC.creator	Umeda, Tomio
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2007-03
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/4372
DC.date" scheme="DCTERMS.W3CDTF	2007-03
DCTERMS.abstract	Representation formulas of the solutions to the Cauchy problems for first order systems of the forms ∂u/∂t - Σ_(j=1)^(d)A_j(t)∂u/∂x_j - A_0(t)u = f are established. The coefficients A_j's are assumed to be matrix-valued functions of the forms A_j(t) = α_j(t)I +β_j(t)M_j, where α_j (t),β_j(t), j = 1,...,d, are real-valued continuous functions, the eigenvalues of the matrices M_j, j = 1,...,d, are real, and the commutators [M_j, M_l] = 0 for all j, l = 0, 1,...,d. No restrictions on the multiplicities of the characteristic roots are imposed.
DC.identifier	info:doi/10.18910/4372
citation_title	Representation formulas of the solutions to the Cauchy problems for first order systems
citation_author	Tajiri, Masaki
citation_author	Umeda, Tomio
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2007-03
citation_journal_title	Osaka Journal of Mathematics
citation_volume	44
citation_issue	1
citation_firstpage	197
citation_lastpage	205
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/4372
citation_doi	info:doi/10.18910/4372

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