Non Local Mixed Systems with Neumann Boundary Conditions

We prove well posedness and stability in ${\mathbf{L}}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the hyperbolic equation is standard, the extension to ${\mathbf{L}}^1$ of classical results about parabolic equations with Neumann conditions is here achieved.