Kinetic solutions for nonlocal stochastic conservation laws-Reference-Cited by-同舟云学术

Kinetic solutions for nonlocal stochastic conservation laws

Published:2021-04-01 Issue:2 Volume:24 Page:559-584
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Lv Guangying¹,Gao Hongjun²,Wei Jinlong³

Affiliation:

1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology , Nanjing , 210044 , P.R. China

2. School of Mathematics, Southeast University , Nanjing , Jiangsu 210023 , P.R. China

3. School of Statistics and Mathematics, Zhongnan University of Economics and Law Wuhan , Hubei , 430073 , P.R. China

Abstract

Abstract This work is devoted to examining the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator and a multiplicative noise. Our proof for uniqueness is based upon the analysis on double variables method and the existence is enabled by a parabolic approximation.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2021-0025/pdf

Reference26 articles.

1. N. Alibaud, Entropy formulation for fractal conservation laws. J. Evol. Equ. 7, No 1 (2007), 145–175.

2. C. Bauzet, G. Vallet and P. Wittbold, The Cauchy problem for a conservation law with a multiplicative stochastic perturbation. J. Hyperbolic Differential Equations 9, No 4 (2012), 661–709.

3. C. Bauzet, G. Vallet and P. Wittbold, The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation. J. Funct. Anal. 266, No 4 (2014), 2503–2545.

4. I. Biswas and A. Majee, Stochastic conservation laws: weak-in-time formulation and strong entropy condition. J. Funct. Anal. 267, No 7 (2014), 2199–2252.

5. G.Q. Chen, Q. Ding and K.H. Karlsen, On nonlinear stochastic balance laws. Arch. Ration. Mech. Anal. 204, No 3 (2012), 707–743.

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