Suprio Bhar, Imran H. Biswas, Saibal Khan, G. Vallet
{"title":"Kolmogorov continuity and stability of sample paths of entropy solutions of stochastic conservation laws","authors":"Suprio Bhar, Imran H. Biswas, Saibal Khan, G. Vallet","doi":"10.1142/s0219891623500091","DOIUrl":null,"url":null,"abstract":"This paper is concerned with sample paths and path-based properties of the entropy solution to conservation laws with stochastic forcing. We derive a series of uniform maximal-type estimates for the viscous perturbation and establish the existence of stochastic entropy solution that has Hölder continuous sample paths. This information is then carefully choreographed with Kružkov’s technique to obtain stronger continuous dependence estimates, based on the nonlinearities, for the sample paths of the solutions. Finally, convergence of sample paths is established for vanishing viscosity approximation along with an explicit rate of convergence.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-06-01","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/s0219891623500091","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with sample paths and path-based properties of the entropy solution to conservation laws with stochastic forcing. We derive a series of uniform maximal-type estimates for the viscous perturbation and establish the existence of stochastic entropy solution that has Hölder continuous sample paths. This information is then carefully choreographed with Kružkov’s technique to obtain stronger continuous dependence estimates, based on the nonlinearities, for the sample paths of the solutions. Finally, convergence of sample paths is established for vanishing viscosity approximation along with an explicit rate of convergence.
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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