scholarly journals On stochastic conservation laws and Malliavin calculus

2017 ◽  
Vol 272 (2) ◽  
pp. 421-497 ◽  
Author(s):  
K.H. Karlsen ◽  
E.B. Storrøsten
Keyword(s):  
Conservation Laws ◽  
Malliavin Calculus ◽  
Stochastic Conservation Laws

scholarly journals Kinetic solutions for nonlocal stochastic conservation laws

2021 ◽  
Vol 24 (2) ◽  
pp. 559-584
Author(s):  
Guangying Lv ◽  
Hongjun Gao ◽  
Jinlong Wei
Keyword(s):  
Conservation Laws ◽  
Multiplicative Noise ◽  
Parabolic Approximation ◽  
Scalar Conservation Laws ◽  
Diffusion Operator ◽  
Stochastic Conservation Laws ◽  
Uniqueness And Existence ◽  
Scalar Conservation

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.

scholarly journals Numerical approximation of stochastic conservation laws on bounded domains

2016 ◽  
Vol 51 (1) ◽  
pp. 225-278 ◽  
Author(s):  
Caroline Bauzet ◽  
Julia Charrier ◽  
Thierry Gallouët
Keyword(s):  
Conservation Laws ◽  
Entropy Solution ◽  
Finite Volume Methods ◽  
Uniqueness Result ◽  
Dirichlet Boundary Conditions ◽  
Stochastic Force ◽  
Stochastic Conservation Laws ◽  
Weak Entropy Solution ◽  
Scalar Conservation ◽  
Continuous Problem

This paper is devoted to the study of finite volume methods for the discretization of scalar conservation laws with a multiplicative stochastic force defined on a bounded domain D of Rd with Dirichlet boundary conditions and a given initial data in L∞(D). We introduce a notion of stochastic entropy process solution which generalizes the concept of weak entropy solution introduced by F.Otto for such kind of hyperbolic bounded value problems in the deterministic case. Using a uniqueness result on this solution, we prove that the numerical solution converges to the unique stochastic entropy weak solution of the continuous problem under a stability condition on the time and space steps.

Sign in / Sign up

Export Citation Format

Share Document