Let L be a second-order partial differential operator in R e. Let R e be the finite union of disjoint polyhedra. Suppose that the diffusion matrix is everywhere non singular and constant on each polyhedron, and that the drift coefficient is bounded and measurable. We show that the martingale problem associated with L is well-posed.

We study the global existence of classical solutions to volume–surface reaction–diffusion systems with control mass. Such appear naturally from modeling evolution concentrations or densities appearing both in a volume domain and its surface, therefore have attracted considerable attention. Due characteristic coupling, general is challenging issue. In particular, duality method, which powerful d...