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Coincidence between linear and global nonlinear stability of non-constant throughflows via the Rionero “Auxiliary System Method”

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Abstract

A system modeling fluid motions in horizontal porous layers, uniformly heated and salted from below, is analyzed in the case of variable thermal and solutal diffusivities. The boundedness and uniqueness of solutions are shown. A class of non-constant throughflows is found and their stability is analyzed via a new approach. Conditions of global nonlinear stability, in closed form, are obtained.

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Acknowledgments

This paper has been performed under the auspices of the G.N.F.M. of I.N.d.A.M. and Progetto Giovani G.N.F.M. 2013 “Moti fluidi di miscele in strati porosi, immersi in campi termici non isotermi”. The authors thank gratefully Prof. Rionero for having proposed the research and for his helpful suggestions.

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  1. Department of Mathematics and Applications “Renato Caccioppoli”, University of Naples Federico II, Via Cinzia 80126, Naples, Italy

    Florinda Capone & Roberta De Luca

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  1. Florinda Capone
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  2. Roberta De Luca
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Correspondence to Florinda Capone.

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Capone, F., De Luca, R. Coincidence between linear and global nonlinear stability of non-constant throughflows via the Rionero “Auxiliary System Method”. Meccanica 49, 2025–2036 (2014). https://doi.org/10.1007/s11012-014-9920-2

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  • DOI: https://doi.org/10.1007/s11012-014-9920-2

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