Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws
In this article, we study the Riemann problem for a strictly hyperbolic system of conservation laws. The governing system arises in nonlinear elasticity and gas dynamics. The system is one of the examples of a strictly hyperbolic system whose Riemann solution consists of delta shock waves as well as...
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| Veröffentlicht in: | Journal of mathematical physics 2019-05, Vol.60 (5) |
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| creator | Sen, Anupam Raja Sekhar, T. |
| description | In this article, we study the Riemann problem for a strictly hyperbolic system of conservation laws. The governing system arises in nonlinear elasticity and gas dynamics. The system is one of the examples of a strictly hyperbolic system whose Riemann solution consists of delta shock waves as well as classical elementary waves such as shock waves, rarefaction waves, and contact discontinuities. We discuss the existence and uniqueness of the solution of the Riemann problem involving δ-shock wave by using a self-similar vanishing viscosity approach. We show that δ-shock wave is a weak*-limit of L1 solution to some viscous perturbations as the viscosity vanishes. |
| doi_str_mv | 10.1063/1.5092668 |
| format | Article |
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We show that δ-shock wave is a weak*-limit of L1 solution to some viscous perturbations as the viscosity vanishes.</description><subject>Conservation laws</subject><subject>Elasticity</subject><subject>Gas dynamics</subject><subject>Hyperbolic systems</subject><subject>Physics</subject><subject>Rarefaction</subject><subject>Self-similarity</subject><subject>Shock waves</subject><subject>Viscosity</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNqd0E1LAzEQBuAgCtbqwX8Q8KSwNd-bPUr9hIIXPS9pmtDUbbNm0i37793agndPA8MzM7yD0DUlE0oUv6cTSSqmlD5BI0p0VZRK6lM0IoSxggmtz9EFwIoQSrUQI-QfXZMNhmW0X3hnOocNYHCNLyCsQ2MS7gLYCCH3uBk6GfuY8DCQU7C56fGyb12axyZYDD1kt8bRYxs34FJncogb3JgdXKIzbxpwV8c6Rp_PTx_T12L2_vI2fZgVlrMyF9wZQSTz2huppODWzqlRlVZGudJI55gWnmtXCi-ZM4ZLTzwhQiykr4akfIxuDnvbFL-3DnK9itu0GU7WjDGheFVWe3V7UDZFgOR83aawNqmvKan3b6xpfXzjYO8OFmzIv4H-h7uY_mDdLjz_AeWfggA</recordid><startdate>201905</startdate><enddate>201905</enddate><creator>Sen, Anupam</creator><creator>Raja Sekhar, T.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-4785-2134</orcidid><orcidid>https://orcid.org/0000-0003-3463-758X</orcidid></search><sort><creationdate>201905</creationdate><title>Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws</title><author>Sen, Anupam ; Raja Sekhar, T.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-3ea4052f8fa56543ccb1a6986a6e7a5ee284f38e74f52eaa35f0f0044d5f97653</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Conservation laws</topic><topic>Elasticity</topic><topic>Gas dynamics</topic><topic>Hyperbolic systems</topic><topic>Physics</topic><topic>Rarefaction</topic><topic>Self-similarity</topic><topic>Shock waves</topic><topic>Viscosity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sen, Anupam</creatorcontrib><creatorcontrib>Raja Sekhar, T.</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sen, Anupam</au><au>Raja Sekhar, T.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws</atitle><jtitle>Journal of mathematical physics</jtitle><date>2019-05</date><risdate>2019</risdate><volume>60</volume><issue>5</issue><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>In this article, we study the Riemann problem for a strictly hyperbolic system of conservation laws. 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| ispartof | Journal of mathematical physics, 2019-05, Vol.60 (5) |
| issn | 0022-2488 1089-7658 |
| language | eng |
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| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Conservation laws Elasticity Gas dynamics Hyperbolic systems Physics Rarefaction Self-similarity Shock waves Viscosity |
| title | Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws |
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