On the solvability conditions for the diffusion equation with convection terms.

Vitaly Volpert (1) , Vitali Vougalter (2)

1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
2 Department of Mathematics [University of Toronto]

Linear second order elliptic equation describing heat or mass di®usion and convection on a given velocity ¯eld 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 SchrÄodinger type operator, for which solvability con- ditions are obtained in our previous work

Domaines: Equations aux dérivées partielles [math.AP]

Vitaly Volpert, Vitali Vougalter. On the solvability conditions for the diffusion equation with convection terms.. Communications on Pure and Applied Mathematics, 2012, 11 (1), pp.365--373. ⟨hal-00753098⟩