Details

Autor(en) / Beteiligte

• Kaspar, David C.
• Rezakhanlou, Fraydoun

Titel

Scalar conservation laws with monotone pure-jump Markov initial conditions

Ist Teil von

• Probability theory and related fields, 2016-08, Vol.165 (3-4), p.867-899

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2016

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• In 2010 Menon and Srinivasan published a conjecture for the statistical structure of solutions ρ to scalar conservation laws with certain Markov initial conditions, proposing a kinetic equation that should suffice to describe ρ ( x , t ) as a stochastic process in x with t fixed. In this article we verify an analogue of the conjecture for initial conditions which are bounded, monotone, and piecewise constant. Our argument uses a particle system representation of ρ ( x , t ) over 0 ≤ x ≤ L for L > 0 , with a suitable random boundary condition at x = L .