Ricerche di Matematica

, Volume 68, Issue 2, pp 581–595 | Cite as

Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term

  • F. CaponeEmail author
  • R. De Luca
  • M. Vitiello


The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained.


Steady convection Hopf convection Vadasz Soret Stability Porous media 

Mathematics Subject Classification

76E06 76S05 35B35 



This work has been performed under the auspices of the G.N.F.M. of INdAM. One of the authors (R. De Luca) acknowledges Progetto Giovani GNFM 2017 “Analisi dei sistemi biologici complessi”


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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Applications R. CaccioppoliUniversity of Naples Federico IINaplesItaly
  2. 2.Department of Mechanics Mathematics and ManagementPolitecnico di BariBariItaly

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