Scalar conservation laws with fractional stochastic forcing: Existence,uniqueness and invariant measure |
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| Authors: | Bruno Saussereau Ion Lucretiu Stoica |
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| Affiliation: | 1. Laboratoire de Mathématiques de Besançon, CNRS, UMR 6623, 16 Route de Gray, 25030 Besançon cedex, France;2. Institute of Mathematics, “Simion Stoilow” of the Romanian Academy and Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest RO-70109, Romania |
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| Abstract: | We study a fractional stochastic perturbation of a first-order hyperbolic equation of nonlinear type. The existence and uniqueness of the solution are investigated via a Lax–Ole?nik formula. To construct the invariant measure we use two main ingredients. The first one is the notion of a generalized characteristic in the sense of Dafermos. The second one is the fact that the oscillations of the fractional Brownian motion are arbitrarily small for an infinite number of intervals of arbitrary length. |
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