Scalar conservation laws with multiple rough fluxes

@article{Gess2014ScalarCL,
  title={Scalar conservation laws with multiple rough fluxes},
  author={B. Gess and P. Souganidis},
  journal={arXiv: Analysis of PDEs},
  year={2014}
}
  • B. Gess, P. Souganidis
  • Published 2014
  • Mathematics
  • arXiv: Analysis of PDEs
  • 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 Souganidis who considered spatially independent and inhomogeneous fluxes with multiple paths and a single driving singular path respectively. The approach is motivated by the theory of stochastic viscosity solutions which relies on special test functions constructed by inverting locally the flow of… CONTINUE READING
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