## 22 Citations

Scalar conservation laws with multiple rough fluxes

- Mathematics
- 2014

We study pathwise entropy solutions for scalar conservation laws with inhomogeneous fluxes and quasilinear multiplicative rough path dependence. This extends the previous work of Lions, Perthame and…

Scalar conservation laws with rough flux and stochastic forcing

- Mathematics
- 2015

In this paper, we study scalar conservation laws where the flux is driven by a geometric Hölder p-rough path for some $$p\in (2,3)$$p∈(2,3) and the forcing is given by an Itô stochastic integral…

Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions

- Mathematics, Computer ScienceJournal of Hyperbolic Differential Equations
- 2018

An explicit estimate is established for the continuous dependence of stochastic entropy solutions on the flux function and the random source function for heterogeneous scalar conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition.

Uniqueness for stochastic scalar conservation laws on Riemannian manifolds revisited

- MathematicsFilomat
- 2022

We revise a uniqueness question for the scalar conservation law with
stochastic forcing du + divgf(x,u)dt = ?(x,u)dWt, x ? M, t ? 0 on a smooth
compact Riemannian manifold (M,g) whereWt is the…

Long‐Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws

- Mathematics
- 2014

We study the long‐time behavior and regularity of the pathwise entropy solutions to stochastic scalar conservation laws with random‐in‐time spatially homogeneous fluxes and periodic initial data. We…

Large deviations for conservative stochastic PDE and non-equilibrium fluctuations

- Mathematics
- 2019

We identify the large deviations rate function for nonlinear diffusion equations with conservative, nonlinear white noise by proving the $\Gamma$-convergence of rate functions to approximating…

The Burgers’ equation with stochastic transport: shock formation, local and global existence of smooth solutions

- MathematicsNonlinear Differential Equations and Applications NoDEA
- 2019

AbstractIn this work, we examine the solution properties of the Burgers’ equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then…

Well-posedness of nonlinear transport equation by stochastic perturbation

- Mathematics
- 2017

Abstract We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutator…

## References

SHOWING 1-10 OF 56 REFERENCES

Scalar conservation laws with rough (stochastic) fluxes

- Mathematics
- 2013

We develop a pathwise theory for scalar conservation laws with quasilinear multiplicative rough path dependence, a special case being stochastic conservation laws with quasilinear stochastic…

Scalar conservation laws with fractional stochastic forcing: Existence, uniqueness and invariant measure

- Mathematics
- 2012

On a stochastic scalar conservation law

- Mathematics
- 2003

In this paper, we discuss the Cauchy problem for a scalar conservation law with a random noise. When the flux function is quadratic (e.g., Burgers' equation), the well-known existence result of…

Large deviations principles for stochastic scalar conservation laws

- Mathematics
- 2010

Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity.…

Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case

- Mathematics
- 2014

We continue the development of the theory of pathwise stochastic entropy solutions for scalar conservation laws in $${\mathbb {R}}^N$$RN with quasilinear multiplicative “rough path” dependence by…

THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION

- Mathematics
- 2012

We study the Cauchy problem for multi-dimensional nonlinear conservation laws with multiplicative stochastic perturbation. Using the concept of measure-valued solutions and Kruzhkov's entropy…