Probabilistic approximation for a porous medium equation
نویسنده
چکیده
In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle system obtained by increasing reordering from these di usions is proved to solve a stochastic di erential equation with normal re ection. Last, we obtain propagation of chaos for the reordered particles to a probability measure which does not solve the martingale problem but is also linked to the porous medium equation. c © 2000 Elsevier Science B.V. All rights reserved.
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