Vitali Vougalter, Vitaly Volpert
On the solvability conditions for the diffusion equation with 
convection terms
(182K, pdf)

ABSTRACT.  Linear second order elliptic equation describing heat or mass diffusion 
and convection on a given velocity field is considered in R^3. 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 H^2(R^3) for the non self-adjoint problem by relating it to a self-adjoint Schroedinger type 
operator, for which solvability conditions are obtained in our previous 
work.