Communications in Mathematical Sciences

Volume 15 (2017)

Number 4

Transport-collapse scheme for scalar conservation laws: initial-boundary value problem

Pages: 1055 – 1071



Darko Mitrović (Faculty of Mathematics and Natural Sciences, University of Montenegro, Podgorica, Montenegro)

Andrej Novak (Faculty of Electrical Engineering, University of Zagreb, Croatia)


We extend Brenier’s transport collapse scheme on the initial-boundary value problem for scalar conservation laws. It is based on averaging out the solution to the corresponding kinetic equation, and it leads to a new solution concept for the problem under consideration. We also provide numerical examples.


scalar conservation laws, well posedness, mixed problem, transport-collapse scheme, kinetic formulation

2010 Mathematics Subject Classification

35L65, 65M25

Published 16 May 2017