2012/03/17 by Sergio Albeverio, Albeverio, S., Olga Rozanova +1
Economics, Econometrics and Finance · Engineering · Mathematics · #35L65 #35L67 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1203.3901
openalex publication_date 2012/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of singularities formation. Further, we introduce an associated system of balance laws that can be interpreted as describing the motion of a continuum with some specific pressure term. This term arises only after the instant when the solution to the initial Cauchy problem looses its smoothness. Before this instant the system coincides partly with the one known as pressure free gas dynamics.