The homogenization of a scalar conservation law with a highly oscillatory forcing term is studied. Effective equations are derived for the local averages of the oscillatory solutions, together with approximations that correctly represent the phase and the amplitude of the oscillations. A random choice method is also designed, which, as demonstrated by our numerical results, gives the correct local averages without necessarily resolving the small scales. Finally, the homogenization problem with an additional small viscosity term is studied.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Conservation laws
- Random choice methods