Probabilistic interpretation for system of conservation law arising in adhesion particle dynamics |
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| Institution: | 1. Materials, Nanotechnologies and Environment Laboratory, Faculty of Sciences, Mohammed V University of Rabat, 4 Avenue Ibn Battouta, BP: 1014, Rabat, Morocco;2. LERMA, ESIE, College of Engineering, International University of Rabat, 11000 - Sala el Jadida, Technopolis, Morocco |
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| Abstract: | This Note presents a construction of a solution for the nonlinear stochastic differential equation Xt = X0 + ∫0t u0(X0)|Xs]ds, t ≥ 0. The random variable X0 with values in and the function u0 are given. We denote by Pt the probability distribution of Xt and u(x, t) = u0(X0)|Xt = x]. We prove that (Pt, u(·, t), t ≥ 0) is a weak solution for system of conservation law arising in adhesion particle dynamics. |
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