Probabilistic characteristics method for a one-dimensional inviscid scalar conservation law

• 成果类型: Article
• 署名作者: Jourdain, B
• 署名单位: Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 334-360
• 关键词: equation

摘要

in this paper, we are interested in approximating the entropy solution of a one-dimensional inviscid scalar conservation law, starting from an initial condition with bounded variation owing to a system of interacting diffusions. We modify the system of signed particles associated with the parabolic equation obtained from the addition of a viscous term to this equation by killing couples of particles with opposite sign that merge. The sample paths of the corresponding reordered particles can be seen as probabilistic characteristics along which the approximate solution is constant. This enables us to prove that when the viscosity vanishes as the initial number of particles goes to +infinity, the approximate solution converges to the unique entropy solution of the inviscid conservation law. We illustrate this convergence by numerical results.