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17 April 2024 |
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Scalar conservation laws with rough flux and stochastic forcing | Martina Hofmanova
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12 Mar 2015 | Abstract: | In this paper, we study scalar conservation laws where the flux is driven by
a geometric H"older $p$-rough path for some $pin (2,3)$ and the forcing is
given by an It^o stochastic integral driven by a Brownian motion. In
particular, we derive the corresponding kinetic formulation and define an
appropriate notion of kinetic solution. In this context, we are able to
establish well-posedness, i.e. existence, uniqueness and the $L^1$-contraction
property that leads to continuous dependence on initial condition. Our approach
combines tools from rough path analysis, stochastic analysis and theory of
kinetic solutions for conservation laws. As an application, this allows to
cover the case of flux driven for instance by another (independent) Brownian
motion enhanced with L’evy’s stochastic area. | Source: | arXiv, 1503.3631 | Services: | Forum | Review | PDF | Favorites |
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