Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE

@article{Gess2016WellposednessAR,
  title={Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE},
  author={B. Gess and M. Hofmanov{\'a}},
  journal={arXiv: Probability},
  year={2016}
}
  • B. Gess, M. Hofmanová
  • Published 2016
  • Mathematics
  • arXiv: Probability
  • We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full $L^1$ setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an $L^1$-contraction property for the… CONTINUE READING
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    • 1
    • Highly Influenced
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 58 REFERENCES
    Degenerate parabolic stochastic partial differential equations
    • 67
    • PDF
    Stochastic non-isotropic degenerate parabolic–hyperbolic equations
    • 21
    • PDF
    Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations
    • 143
    • PDF
    ON A STOCHASTIC FIRST-ORDER HYPERBOLIC EQUATION IN A BOUNDED DOMAIN
    • 58
    • PDF