On the solvability conditions for the diffusion equation with convection terms

Abstract

A linear second order elliptic equation describing heat or mass diffusion and convection on a given velocity field is considered in R3. The corresponding operator L may not satisfy the Fredholm property. In this case, solvability conditions for the equation Lu = f are not known. In this work, we derive solvability conditions in H2(R3) for the non self-adjoint problem by relating it to a self-adjoint Schrödinger type operator, for which solvability conditions are obtained in our previous work [13].