Variational principles for advection-diffusion problems

Variational principles for linear and semilinear advection-diffusion problems with velocity field given by potential flow are described and analyzed. Mixed Dirichlet and prescribed flux conditions are treated. Existence and uniqueness results are proved and equivalent integral operator equations are found. A positive multiplier function related to the potential of the flow is used to change the system to divergence form. The dependence of the solution on inhomogeneous flux boundary data is determined.