Kinetic Formulation for a Parabolic Conservation Law. Application to Homogenization
Kinetic Formulation for a Parabolic Conservation Law. Application to Homogenization
We derive a kinetic formulation for the parabolic scalar conservation law $\partial_t u + \mathrm{div}_y A(y,u) - \Delta_y u=0$. This allows us to define a weaker notion of solutions in $L^1$, which is enough to recover the $L^1$ contraction principle. We also apply this kinetic formulation to a homogenization problem …