A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem

L. Flodén; A. Holmbom; P. Jonasson; T. Lobkova; M. Olsson Lindberg; Y. Zhang

doi:10.1063/1.4972769

A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem

L. Flodén, A. Holmbom^*, P. Jonasson, T. Lobkova, M. Olsson Lindberg, Y. Zhang

^*此作品的通讯作者

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

摘要

We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ϵ→0. We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ϵ^-1∂_tu_ϵ as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.

源语言	英语
主期刊名	ICNPAA 2016 World Congress
主期刊副标题	11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences
编辑	Seenith Sivasundaram
出版商	American Institute of Physics Inc.
ISBN（电子版）	9780735414648
DOI	https://doi.org/10.1063/1.4972769
出版状态	已出版 - 27 1月 2017
已对外发布	是
活动	11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016 - La Rochelle, 法国期限: 4 7月 2016 → 8 7月 2016

出版系列

姓名	AIP Conference Proceedings
卷	1798
ISSN（印刷版）	0094-243X
ISSN（电子版）	1551-7616

会议

会议	11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016
国家/地区	法国
市	La Rochelle
时期	4/07/16 → 8/07/16

访问文件

10.1063/1.4972769

其它文件与链接

链接到 Scopus 的出版物

引用此

Flodén, L., Holmbom, A., Jonasson, P., Lobkova, T., Lindberg, M. O., & Zhang, Y. (2017). A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem. 在 S. Sivasundaram (编辑), ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences 文章 020177 (AIP Conference Proceedings; 卷 1798). American Institute of Physics Inc.. https://doi.org/10.1063/1.4972769

Flodén, L. ; Holmbom, A. ; Jonasson, P. 等. / A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem. ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. 编辑 / Seenith Sivasundaram. American Institute of Physics Inc., 2017. (AIP Conference Proceedings).

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title = "A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem",

abstract = "We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ϵ→0. We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ϵ-1∂tuϵ as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.",

author = "L. Flod{\'e}n and A. Holmbom and P. Jonasson and T. Lobkova and Lindberg, {M. Olsson} and Y. Zhang",

note = "Publisher Copyright: {\textcopyright} 2017 Author(s).; 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016 ; Conference date: 04-07-2016 Through 08-07-2016",

year = "2017",

month = jan,

day = "27",

doi = "10.1063/1.4972769",

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series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

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Flodén, L, Holmbom, A, Jonasson, P, Lobkova, T, Lindberg, MO & Zhang, Y 2017, A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem. 在 S Sivasundaram (编辑), ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences., 020177, AIP Conference Proceedings, 卷 1798, American Institute of Physics Inc., 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, La Rochelle, 法国, 4/07/16. https://doi.org/10.1063/1.4972769

A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem. / Flodén, L.; Holmbom, A.; Jonasson, P. 等.
ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. 编辑 / Seenith Sivasundaram. American Institute of Physics Inc., 2017. 020177 (AIP Conference Proceedings; 卷 1798).

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

TY - GEN

T1 - A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem

AU - Flodén, L.

AU - Holmbom, A.

AU - Jonasson, P.

AU - Lobkova, T.

AU - Lindberg, M. Olsson

AU - Zhang, Y.

PY - 2017/1/27

Y1 - 2017/1/27

N2 - We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ϵ→0. We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ϵ-1∂tuϵ as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.

AB - We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ϵ→0. We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ϵ-1∂tuϵ as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.

UR - http://www.scopus.com/inward/record.url?scp=85013657168&partnerID=8YFLogxK

U2 - 10.1063/1.4972769

DO - 10.1063/1.4972769

M3 - Conference contribution

AN - SCOPUS:85013657168

T3 - AIP Conference Proceedings

BT - ICNPAA 2016 World Congress

A2 - Sivasundaram, Seenith

PB - American Institute of Physics Inc.

T2 - 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016

Y2 - 4 July 2016 through 8 July 2016

ER -

Flodén L, Holmbom A, Jonasson P, Lobkova T, Lindberg MO, Zhang Y. A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem. 在 Sivasundaram S, 编辑, ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. American Institute of Physics Inc. 2017. 020177. (AIP Conference Proceedings). doi: 10.1063/1.4972769

A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem

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