Communications in Mathematical Sciences
Volume 15 (2017)
Transport-collapse scheme for scalar conservation laws: initial-boundary value problem
Pages: 1055 – 1071
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