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On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels
In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution γ ∗ q , we weaken the standard assumption on the kernel γ ∈ L ∞ ( ( 0 , T ) ; W 1 , ∞ ( R ) ) to the substantially...
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| Published in: | Zeitschrift für angewandte Mathematik und Physik 2022-12, Vol.73 (6), Article 241 |
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| Main Authors: | , , , |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c293t-e6a71143a9c1a8cd1d3a1da4fc73bbdbb6befbbbafb4520c8d39952874728bd03 |
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| container_issue | 6 |
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| container_title | Zeitschrift für angewandte Mathematik und Physik |
| container_volume | 73 |
| creator | Coclite, Giuseppe Maria De Nitti, Nicola Keimer, Alexander Pflug, Lukas |
| description | In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution
γ
∗
q
, we weaken the standard assumption on the kernel
γ
∈
L
∞
(
(
0
,
T
)
;
W
1
,
∞
(
R
)
)
to the substantially more general condition
γ
∈
L
∞
(
(
0
,
T
)
;
B
V
(
R
)
)
, which allows for discontinuities in the kernel. |
| doi_str_mv | 10.1007/s00033-022-01766-0 |
| format | article |
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γ
∗
q
, we weaken the standard assumption on the kernel
γ
∈
L
∞
(
(
0
,
T
)
;
W
1
,
∞
(
R
)
)
to the substantially more general condition
γ
∈
L
∞
(
(
0
,
T
)
;
B
V
(
R
)
)
, which allows for discontinuities in the kernel.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-022-01766-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Conservation laws ; Engineering ; Kernels ; Mathematical Methods in Physics ; Theoretical and Applied Mechanics ; Uniqueness</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2022-12, Vol.73 (6), Article 241</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c293t-e6a71143a9c1a8cd1d3a1da4fc73bbdbb6befbbbafb4520c8d39952874728bd03</citedby><cites>FETCH-LOGICAL-c293t-e6a71143a9c1a8cd1d3a1da4fc73bbdbb6befbbbafb4520c8d39952874728bd03</cites><orcidid>0000-0001-6019-4757 ; 0000-0001-8001-5832 ; 0000-0003-0402-7502 ; 0000-0003-3825-5853</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Coclite, Giuseppe Maria</creatorcontrib><creatorcontrib>De Nitti, Nicola</creatorcontrib><creatorcontrib>Keimer, Alexander</creatorcontrib><creatorcontrib>Pflug, Lukas</creatorcontrib><title>On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution
γ
∗
q
, we weaken the standard assumption on the kernel
γ
∈
L
∞
(
(
0
,
T
)
;
W
1
,
∞
(
R
)
)
to the substantially more general condition
γ
∈
L
∞
(
(
0
,
T
)
;
B
V
(
R
)
)
, which allows for discontinuities in the kernel.</description><subject>Conservation laws</subject><subject>Engineering</subject><subject>Kernels</subject><subject>Mathematical Methods in Physics</subject><subject>Theoretical and Applied Mechanics</subject><subject>Uniqueness</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwB5gsMRvOdhInI1R8SZW6AAuDZTsOpA12sRMC_x6XILExnXT33HunB6FTCucUQFxEAOCcAGMEqCgKAntoRjMGpAJe7aMZQJYRxkR-iI5iXCdcUOAz9Lxy2H62sbfOWKxcjQfXvg_W2Rixb_Bo1QZH3w19613EvcfOu84b1WGTGjZ8qN0Ed2qMeGz7V3z1hDc2ONvFY3TQqC7ak986R4831w-LO7Jc3d4vLpfEsIr3xBZKUJpxVRmqSlPTmitaq6wxgmtda11o22itVaOznIEpa15VOStFJlipa-BzdDblboNPr8derv0QXDopmWBVniecJ4pNlAk-xmAbuQ3tmwpfkoLcSZSTRJkkyh-JchfNp6WYYPdiw1_0P1vfGwd2ag</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Coclite, Giuseppe Maria</creator><creator>De Nitti, Nicola</creator><creator>Keimer, Alexander</creator><creator>Pflug, Lukas</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-6019-4757</orcidid><orcidid>https://orcid.org/0000-0001-8001-5832</orcidid><orcidid>https://orcid.org/0000-0003-0402-7502</orcidid><orcidid>https://orcid.org/0000-0003-3825-5853</orcidid></search><sort><creationdate>20221201</creationdate><title>On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels</title><author>Coclite, Giuseppe Maria ; De Nitti, Nicola ; Keimer, Alexander ; Pflug, Lukas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c293t-e6a71143a9c1a8cd1d3a1da4fc73bbdbb6befbbbafb4520c8d39952874728bd03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Conservation laws</topic><topic>Engineering</topic><topic>Kernels</topic><topic>Mathematical Methods in Physics</topic><topic>Theoretical and Applied Mechanics</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Coclite, Giuseppe Maria</creatorcontrib><creatorcontrib>De Nitti, Nicola</creatorcontrib><creatorcontrib>Keimer, Alexander</creatorcontrib><creatorcontrib>Pflug, Lukas</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</collection><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Coclite, Giuseppe Maria</au><au>De Nitti, Nicola</au><au>Keimer, Alexander</au><au>Pflug, Lukas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>73</volume><issue>6</issue><artnum>241</artnum><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution
γ
∗
q
, we weaken the standard assumption on the kernel
γ
∈
L
∞
(
(
0
,
T
)
;
W
1
,
∞
(
R
)
)
to the substantially more general condition
γ
∈
L
∞
(
(
0
,
T
)
;
B
V
(
R
)
)
, which allows for discontinuities in the kernel.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-022-01766-0</doi><orcidid>https://orcid.org/0000-0001-6019-4757</orcidid><orcidid>https://orcid.org/0000-0001-8001-5832</orcidid><orcidid>https://orcid.org/0000-0003-0402-7502</orcidid><orcidid>https://orcid.org/0000-0003-3825-5853</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0044-2275 |
| ispartof | Zeitschrift für angewandte Mathematik und Physik, 2022-12, Vol.73 (6), Article 241 |
| issn | 0044-2275 1420-9039 |
| language | eng |
| recordid | cdi_proquest_journals_2729559953 |
| source | Springer Nature |
| subjects | Conservation laws Engineering Kernels Mathematical Methods in Physics Theoretical and Applied Mechanics Uniqueness |
| title | On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels |
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