Riemann Problem and Wave Interactions for a Temple-class Hyperbolic System of Conservation Laws
The exact solutions of the Riemann problem for a Temple-class hyperbolic system of conservation laws consisting of three scalar equations are obtained in fully explicit forms, in which all the state variables may contain Dirac delta functions simultaneously under some suitable Riemann initial data....
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2021-11, Vol.44 (6), p.4195-4221 |
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| container_title | Bulletin of the Malaysian Mathematical Sciences Society |
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| creator | Wei, Zhijian Sun, Meina |
| description | The exact solutions of the Riemann problem for a Temple-class hyperbolic system of conservation laws consisting of three scalar equations are obtained in fully explicit forms, in which all the state variables may contain Dirac delta functions simultaneously under some suitable Riemann initial data. The generalized Rankine–Hugoniot conditions and the over-compressive entropy condition are derived for such very singular delta shock wave solution. We also prove rigorously this delta shock wave solution satisfying the system in the sense of distributions. Moreover, three typical cases for the delta shock interaction problem are provided in order to illustrate some interesting nonlinear wave phenomena. In addition, some numerical simulations are offered to confirm the theoretical results. |
| doi_str_mv | 10.1007/s40840-021-01161-4 |
| format | Article |
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The generalized Rankine–Hugoniot conditions and the over-compressive entropy condition are derived for such very singular delta shock wave solution. We also prove rigorously this delta shock wave solution satisfying the system in the sense of distributions. Moreover, three typical cases for the delta shock interaction problem are provided in order to illustrate some interesting nonlinear wave phenomena. 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Malays. Math. Sci. Soc</addtitle><description>The exact solutions of the Riemann problem for a Temple-class hyperbolic system of conservation laws consisting of three scalar equations are obtained in fully explicit forms, in which all the state variables may contain Dirac delta functions simultaneously under some suitable Riemann initial data. The generalized Rankine–Hugoniot conditions and the over-compressive entropy condition are derived for such very singular delta shock wave solution. We also prove rigorously this delta shock wave solution satisfying the system in the sense of distributions. Moreover, three typical cases for the delta shock interaction problem are provided in order to illustrate some interesting nonlinear wave phenomena. In addition, some numerical simulations are offered to confirm the theoretical results.</description><subject>Applications of Mathematics</subject><subject>Cauchy problems</subject><subject>Conservation laws</subject><subject>Delta function</subject><subject>Exact solutions</subject><subject>Hyperbolic systems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Shock waves</subject><subject>Wave interaction</subject><issn>0126-6705</issn><issn>2180-4206</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWLR_wFPAc3SSzWZ3j1LUFgqKVjyG7GYiW_bLZFvpvzd1BW_OZRh4n3fgIeSKww0HyG6DhFwCA8EZcK44kydkJngOTApQp2QGXCimMkjPyTyELcRJlVCCz4h-qbE1XUeffV822FLTWfpu9khX3YjeVGPdd4G63lNDN9gODbKqMSHQ5WFAX_ZNXdHXQxgj2ju6iGH0e3Ok6Np8hUty5kwTcP67L8jbw_1msWTrp8fV4m7NKpHByBILVqU2Lw1CopQsXAJZkaNwUCRWZsZYpxzmqiqshURiURoZD1miQuBVckGup97B9587DKPe9jvfxZdapFmRRUMJjykxpSrfh-DR6cHXrfEHzUEfXerJpY4u9Y9LLSOUTFCI4e4D_V_1P9Q30hZ3JA</recordid><startdate>20211101</startdate><enddate>20211101</enddate><creator>Wei, Zhijian</creator><creator>Sun, Meina</creator><general>Springer Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-6483-6497</orcidid></search><sort><creationdate>20211101</creationdate><title>Riemann Problem and Wave Interactions for a Temple-class Hyperbolic System of Conservation Laws</title><author>Wei, Zhijian ; Sun, Meina</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-3d0d65d8bae036649f30798e2f093d47aadf6fe86c9dd034e9ba46c94be6e01c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applications of Mathematics</topic><topic>Cauchy problems</topic><topic>Conservation laws</topic><topic>Delta function</topic><topic>Exact solutions</topic><topic>Hyperbolic systems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Shock waves</topic><topic>Wave interaction</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wei, Zhijian</creatorcontrib><creatorcontrib>Sun, Meina</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wei, Zhijian</au><au>Sun, Meina</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Riemann Problem and Wave Interactions for a Temple-class Hyperbolic System of Conservation Laws</atitle><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle><stitle>Bull. Malays. Math. Sci. Soc</stitle><date>2021-11-01</date><risdate>2021</risdate><volume>44</volume><issue>6</issue><spage>4195</spage><epage>4221</epage><pages>4195-4221</pages><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>The exact solutions of the Riemann problem for a Temple-class hyperbolic system of conservation laws consisting of three scalar equations are obtained in fully explicit forms, in which all the state variables may contain Dirac delta functions simultaneously under some suitable Riemann initial data. The generalized Rankine–Hugoniot conditions and the over-compressive entropy condition are derived for such very singular delta shock wave solution. We also prove rigorously this delta shock wave solution satisfying the system in the sense of distributions. Moreover, three typical cases for the delta shock interaction problem are provided in order to illustrate some interesting nonlinear wave phenomena. 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| source | Springer Nature - Complete Springer Journals |
| subjects | Applications of Mathematics Cauchy problems Conservation laws Delta function Exact solutions Hyperbolic systems Mathematics Mathematics and Statistics Shock waves Wave interaction |
| title | Riemann Problem and Wave Interactions for a Temple-class Hyperbolic System of Conservation Laws |
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