Abstract
We present some results concerning stochastic linear transport equations and quasilinear scalar conservation laws, where the additive noise is a perturbation of the drift. Due to the introduction of the stochastic term, we may prove for instance well-posedness for continuity equation (divergence-free), Cauchy problem, meanwhile uniqueness may fail for the deterministic case, see [1], [2] and [6]. Also for the transport equation, Dirichlet data, we established a better trace result by the introduction of the noise, show existence and uniqueness in a general context, see [7]. We introduce the study of stochastic hyperbolic conservation laws, in a dierent direction of [5], applying the kinetic-semigroup theory.
References
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