2010/11/13 by Nadia Belaribi, Belaribi, Nadia, François Cuvelier +4
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1011.3107
The object of this paper is a one-dimensional generalized porous media\nequation (PDE) with possibly discontinuous coefficient \β, which is\nwell-posed as an evolution problem in L1(\ℝ). In some recent papers\nof Blanchard et alia and Barbu et alia, the solution was represented by the\nsolution of a non-linear stochastic differential equation in law if the initial\ncondition is a bounded integrable function. We first extend this result, at\nleast when \β is continuous and the initial condition is only integrable\nwith some supplementary technical assumption. The main purpose of the article\nconsists in introducing and implementing a stochastic particle algorithm to\napproach the solution to (PDE) which also fits in the case when \β is\npossibly irregular, to predict some long-time behavior of the solution and in\ncomparing with some recent numerical deterministic techniques.\n