{"title":"标量守恒定律的Lp压缩解","authors":"Kihito Hinohara, Natsuki Minagawa, Hiroki Ohwa, Hiroya Suzuki, Shou Ukita","doi":"10.1142/s0219891622500059","DOIUrl":null,"url":null,"abstract":"We estimate the [Formula: see text] distance between piecewise constant solutions to the Cauchy problem of scalar conservation laws and propose a sufficient condition for having an [Formula: see text] contraction of such solutions. Moreover, we prove that there exist [Formula: see text] contractive solutions on a set of all monotone bounded initial functions to the Cauchy problem of scalar conservation laws with convex or concave flux functions.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Lp Contractive solutions for scalar conservation laws\",\"authors\":\"Kihito Hinohara, Natsuki Minagawa, Hiroki Ohwa, Hiroya Suzuki, Shou Ukita\",\"doi\":\"10.1142/s0219891622500059\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We estimate the [Formula: see text] distance between piecewise constant solutions to the Cauchy problem of scalar conservation laws and propose a sufficient condition for having an [Formula: see text] contraction of such solutions. Moreover, we prove that there exist [Formula: see text] contractive solutions on a set of all monotone bounded initial functions to the Cauchy problem of scalar conservation laws with convex or concave flux functions.\",\"PeriodicalId\":50182,\"journal\":{\"name\":\"Journal of Hyperbolic Differential Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Hyperbolic Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219891622500059\",\"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/s0219891622500059","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Lp Contractive solutions for scalar conservation laws
We estimate the [Formula: see text] distance between piecewise constant solutions to the Cauchy problem of scalar conservation laws and propose a sufficient condition for having an [Formula: see text] contraction of such solutions. Moreover, we prove that there exist [Formula: see text] contractive solutions on a set of all monotone bounded initial functions to the Cauchy problem of scalar conservation laws with convex or concave flux functions.
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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