Stochastic scalar conservation laws driven by rough paths

@article{Friz2014StochasticSC,
  title={Stochastic scalar conservation laws driven by rough paths},
  author={Peter K. Friz and Benjamin Gess},
  journal={arXiv: Analysis of PDEs},
  year={2014}
}
  • P. Friz, B. Gess
  • Published 26 March 2014
  • Mathematics
  • arXiv: Analysis of PDEs
View PDF on arXiv
22 Citations
Highly Influential Citations
1
Background Citations
6
Methods Citations
6
Results Citations
2

22 Citations

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Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
  • G. Lv, Jiang-Lun Wu
  • Mathematics, Computer Science
    Journal of Hyperbolic Differential Equations
  • 2018
TLDR
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Long‐Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws
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Abstract We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutator…
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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
Partial differential equations driven by rough paths
On a stochastic scalar conservation law
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…
Stochastic scalar conservation laws
Large deviations principles for stochastic scalar conservation laws
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
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…
Degenerate parabolic stochastic partial differential equations
THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION
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