{"title":"双曲守恒律中的最优跳集","authors":"Shyam Sundar Ghoshal, A. Jana","doi":"10.1142/S021989162050023X","DOIUrl":null,"url":null,"abstract":"We investigate qualitative properties of entropy solutions to hyperbolic conservation laws, and construct an entropy solution to a scalar conservation law for which the jump set is not closed, in particular, it is dense in a space-time domain. In a second part, we establish a similar result for hyperbolic systems. We give two different approaches for scalar conservation laws and hyperbolic systems in order to obtain these results. For the scalar case, the solutions are explicitly calculated.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2019-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal jump set in hyperbolic conservation laws\",\"authors\":\"Shyam Sundar Ghoshal, A. Jana\",\"doi\":\"10.1142/S021989162050023X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate qualitative properties of entropy solutions to hyperbolic conservation laws, and construct an entropy solution to a scalar conservation law for which the jump set is not closed, in particular, it is dense in a space-time domain. In a second part, we establish a similar result for hyperbolic systems. We give two different approaches for scalar conservation laws and hyperbolic systems in order to obtain these results. For the scalar case, the solutions are explicitly calculated.\",\"PeriodicalId\":50182,\"journal\":{\"name\":\"Journal of Hyperbolic Differential Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Hyperbolic Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S021989162050023X\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Hyperbolic Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S021989162050023X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
We investigate qualitative properties of entropy solutions to hyperbolic conservation laws, and construct an entropy solution to a scalar conservation law for which the jump set is not closed, in particular, it is dense in a space-time domain. In a second part, we establish a similar result for hyperbolic systems. We give two different approaches for scalar conservation laws and hyperbolic systems in order to obtain these results. For the scalar case, the solutions are explicitly calculated.
期刊介绍：
This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in:
Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions.
Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc.
Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations.
Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc.
General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations.
Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.
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