GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR SOLUTIONS TO THE CAUCHY PROBLEM OF THE SCALAR CONSERVATION LAW WITH NONLINEAR VISCOSITY

Matsumura, Akitaka; Yoshida, Natsumi

doi:https://doi.org/10.18910/73745

GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR SOLUTIONS TO THE CAUCHY PROBLEM OF THE SCALAR CONSERVATION LAW WITH NONLINEAR VISCOSITY

Matsumura, Akitaka; Yoshida, Natsumi

Osaka Journal of Mathematics, 2020, 57(1), 187-205

アクセス数:438件（2026-09-09 06:53 集計）

固定URL: https://doi.org/10.18910/73745

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タイトル	GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR SOLUTIONS TO THE CAUCHY PROBLEM OF THE SCALAR CONSERVATION LAW WITH NONLINEAR VISCOSITY
著者	NRID 1000060115938 1000060115938 著者名 Matsumura, Akitaka
著者	著者名 Yoshida, Natsumi
抄録	In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	57(1)
ページ	187-205
刊行年月	2020-01
言語	英語
ハンドルURL	https://hdl.handle.net/11094/73745
DOI	https://doi.org/10.18910/73745
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 57, Number 1 （2020-1）

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. 2020, 57(1), p. 187-205
DC.title	GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR SOLUTIONS TO THE CAUCHY PROBLEM OF THE SCALAR CONSERVATION LAW WITH NONLINEAR VISCOSITY
DC.creator	Matsumura, Akitaka
DC.creator	Yoshida, Natsumi
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2020-01
DCTERMS.abstract	In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.
DC.identifier	10.18910/73745
DC.format	73745
citation_title	GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR SOLUTIONS TO THE CAUCHY PROBLEM OF THE SCALAR CONSERVATION LAW WITH NONLINEAR VISCOSITY
citation_author	Matsumura, Akitaka
citation_author	Yoshida, Natsumi
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2020-01
citation_journal_title	Osaka Journal of Mathematics
citation_volume	57
citation_issue	1
citation_firstpage	187
citation_lastpage	205
citation_public_url	https://hdl.handle.net/11094/73745
citation_doi_detail	10.18910/73745
citation_doi	https://doi.org/10.18910/73745

GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR SOLUTIONS TO THE CAUCHY PROBLEM OF THE SCALAR CONSERVATION LAW WITH NONLINEAR VISCOSITY

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