Functional Solutions for Fluid Flows Through Porous Media

Giovanni Cimatti

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 1, page 187-200
  • ISSN: 0392-4041

Abstract

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The Levy-Caccioppoli global inversion theorem is applied to prove the existence and uniqueness of functional solutions for a problem of flow of a viscous incompressible fluid in a porous medium when the viscosity and the thermal conductivity depend on the temperature. A method based on the Abel integral equation, for determining the dependence of the viscosity from the temperature is also proposed.

How to cite

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Cimatti, Giovanni. "Functional Solutions for Fluid Flows Through Porous Media." Bollettino dell'Unione Matematica Italiana 5.1 (2012): 187-200. <http://eudml.org/doc/290851>.

@article{Cimatti2012,
abstract = {The Levy-Caccioppoli global inversion theorem is applied to prove the existence and uniqueness of functional solutions for a problem of flow of a viscous incompressible fluid in a porous medium when the viscosity and the thermal conductivity depend on the temperature. A method based on the Abel integral equation, for determining the dependence of the viscosity from the temperature is also proposed.},
author = {Cimatti, Giovanni},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {187-200},
publisher = {Unione Matematica Italiana},
title = {Functional Solutions for Fluid Flows Through Porous Media},
url = {http://eudml.org/doc/290851},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Cimatti, Giovanni
TI - Functional Solutions for Fluid Flows Through Porous Media
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/2//
PB - Unione Matematica Italiana
VL - 5
IS - 1
SP - 187
EP - 200
AB - The Levy-Caccioppoli global inversion theorem is applied to prove the existence and uniqueness of functional solutions for a problem of flow of a viscous incompressible fluid in a porous medium when the viscosity and the thermal conductivity depend on the temperature. A method based on the Abel integral equation, for determining the dependence of the viscosity from the temperature is also proposed.
LA - eng
UR - http://eudml.org/doc/290851
ER -

References

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  1. ABEL, N. H., Résolution d'un problém de mécanique, Journal für die reine and angewandte Mathematik, herausgegeben von Crelle, 1, Berlin (1826), 97-101. 
  2. AMBROSETTI, A. - PRODI, G., Nonlinear Analysis, Cambridge University Press, 1993. 
  3. BEAR, J., Dynamics of Fluids in Porous Media, Dover Publications, Inc.New York, 1988. Zbl1191.76002
  4. CACCIOPPOLI, R., Un principio di inversione per le corrispondenze funzionali, Atti Accad. Naz. Lincei, 16 (1932), 392-400. 
  5. CIMATTI, G., On the functional solutions of a system of partial differential equations relevant in mathematical physics, Rend. Mat. Univ. Parma, 10 (2010), 423-439. Zbl1216.35022MR2789450
  6. CIMATTI, G., Application of the Abel integral equation to an inverse problem in thermoelectricity, Eur. Jour. Appl. Math (to appear). Zbl1180.80013MR2558705DOI10.1017/S095679250999009X
  7. GORENFLO, R. - VESSELLA, S., Abel Integral Equations, Springer-Verlag, Berlin, 1980. MR1095269DOI10.1007/BFb0084665
  8. LEVY, P., Sur les functions de lignes implicites, Bull. Soc. Mat. Fr., 48, 13-27. Zbl47.0381.01MR1504790
  9. NIELD, D. A. - BEJAN, A., Convection in Porous Media, Springer Verlag, Berlin, 1998. Zbl1268.76001MR1656781DOI10.1007/978-1-4757-3033-3
  10. PROTTER, M. - WEINBERGER, H., Maximus Principle in Differential Equations, Springer-Verlag, New York, 1963. MR762825DOI10.1007/978-1-4612-5282-5
  11. TONELLI, L., Su un problema di Abel, Math. Ann.99 (1928), 183-199. MR1512447DOI10.1007/BF01459094
  12. TRICOMI, F. G., Integral Equations, Interscience Publishers, London1957. MR94665

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