Hierarchies of N-point functions for nonlinear conservation laws with random initial data

Carey Caginalp

Physica A: Statistical Mechanics and its Applications, 2018, vol. 503, issue C, 727-744

Abstract: Nonlinear conservation laws subject to random initial conditions pose fundamental problems in the evolution and interactions of shocks and rarefactions. Using a discrete set of values for the solution, we derive a hierarchy of equations in terms of the states in two different methods. This hierarchy involves the n-point function, the probability that the solution takes on various values at different positions, in terms of the (n+1)-point function. In the first approach, these equations can be closed but the resulting solutions do not persist through shock interactions. In our second approach, the n-point function is expressed in terms of the (n+1)-point functions, and remains valid through collisions of shocks.

Keywords: Partial differential equations; Stochastics; Randomness (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:503:y:2018:i:c:p:727-744

DOI: 10.1016/j.physa.2018.03.008

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