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
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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
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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
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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.
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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
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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
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