  We study a second-order parabolic equation with divergence form elliptic
operator, having piecewise constant diffusion coefficients with two points of
discontinuity. Such partial differential equations appear in the modelization
of diffusion phenomena in medium consisting of three kind of materials. Using
probabilistic methods, we present an explicit expression of the fundamental
solution under certain conditions. We also derive small-time asymptotic
expansion of the PDE's solutions in the general case. The obtained results are
directly usable in applications.
