673	RWTH Publication No: 1002851        2025
TITLE	Solving Random Hyperbolic Conservation Laws Using Linear Programming
AUTHORS	Shaoshuai Chu, Michael Herty, Maria Lukacova-Medvid'ova, Yizhou Zhou
ABSTRACT	A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial differential equation with respect to the Young measure and allows to compute the approximation based on linear programming problems. We analyze the structure-preserving properties of the derived numerical method and discuss its advantages and disadvantages. Numerical results for one-dimensional Burgers equation and the isentropic Euler equations and comparisons with stochastic collocation method illustrate the behavior of the proposed numerical method.
KEYWORDS	nonlinear hyperbolic systems with uncertainty, Random parameterized Young measures, Moment closure problems