Extension of joseph's criterion to the nonlinear stability of mechanical equilibria in the presence of thermodiffusive conductivity

Joseph's criterion from 1] is extended to the case of thermodiffusive conductivity for a fluid layer subject to several competing (stabilizing and destabilizing) effects. Criterion for the uniqueness and stability of all (eight) physical parameters involved was obtained. In this way, for a more realistic mathematical model, physically relevant bounds for the domain of stability are achieved.This work was performed under the auspices of G.N.F.M.-C.N.R. and I.R.M.A.-C.N.R. and was supported by M.U.R.S.T. under the grant 60% Algebra lineare ed equationi alle derivate parziali in the framework of Professor R. Pelluso's group, University of Bari, Italy.