On a system of equations of evolution with a non-symmetrical parabolic part occuring in the analysis of moisture and heat transfer in porous media

Jiří Vala

Applications of Mathematics (2002)

  • Volume: 47, Issue: 2, page 187-214
  • ISSN: 0862-7940

Abstract

top
Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jäger and J. Kačur). In this paper the general variational formulation of the corresponding system is presented and its existence and convergence properties are verified; its application to one model problem (preserving the symmetry in the elliptic, but not in the parabolic part) is demonstrated.

How to cite

top

Vala, Jiří. "On a system of equations of evolution with a non-symmetrical parabolic part occuring in the analysis of moisture and heat transfer in porous media." Applications of Mathematics 47.2 (2002): 187-214. <http://eudml.org/doc/33112>.

@article{Vala2002,
abstract = {Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jäger and J. Kačur). In this paper the general variational formulation of the corresponding system is presented and its existence and convergence properties are verified; its application to one model problem (preserving the symmetry in the elliptic, but not in the parabolic part) is demonstrated.},
author = {Vala, Jiří},
journal = {Applications of Mathematics},
keywords = {PDE’s of evolution; method of Rothe; porous media; moisture and heat transfer; full parabolic system; nonlinear parabolic system},
language = {eng},
number = {2},
pages = {187-214},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a system of equations of evolution with a non-symmetrical parabolic part occuring in the analysis of moisture and heat transfer in porous media},
url = {http://eudml.org/doc/33112},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Vala, Jiří
TI - On a system of equations of evolution with a non-symmetrical parabolic part occuring in the analysis of moisture and heat transfer in porous media
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 2
SP - 187
EP - 214
AB - Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jäger and J. Kačur). In this paper the general variational formulation of the corresponding system is presented and its existence and convergence properties are verified; its application to one model problem (preserving the symmetry in the elliptic, but not in the parabolic part) is demonstrated.
LA - eng
KW - PDE’s of evolution; method of Rothe; porous media; moisture and heat transfer; full parabolic system; nonlinear parabolic system
UR - http://eudml.org/doc/33112
ER -

References

top
  1. Nonlinear Superposition Operators, Cambridge University Press, 1980. (1980) MR1066204
  2. The Kiessl model, existence of classical solution, In: Proceedings of the conference “Matematická štatistika, numerická matematika a ich aplikácie”, Kočovce (Slovak Republic),  (eds.), 1999, pp. 62–75. (Slovak) (1999) 
  3. 10.1023/A:1022232632054, Appl. Math. 45 (2000), 3–17. (2000) MR1738893DOI10.1023/A:1022232632054
  4. A model of moisture and temperature propagation, Preprint, Technical University (Faculty of Civil Engineering) in Brno, 2000. (2000) 
  5. Monotone operators—a survey directed to differential equations, Appl. Math. 35 (1991), 257–300. (1991) MR1065003
  6. Weakly continuous operators—applications to differential equations, Appl. Math. 39 (1994), 45–56. (1994) MR1254746
  7. Nonlinear Differential Equations, Elsevier, Amsterdam, 1980. (1980) MR0558764
  8. Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie Verlag, Berlin, 1974. (1974) MR0636412
  9. Wärmeleitung und Feuchtigkeitdurchgang durch Kühlraumisolierungen, Kältetechnik H.3 (1958), 86–91. (1958) 
  10. 10.1007/BF01385729, Numer. Math. 60 (1991), 407–427. (1991) MR1137200DOI10.1007/BF01385729
  11. Approximation of porous medium type systems by nondegenerate elliptic systems, Stochastische mathematische Modelle, Preprint 123, University of Heidelberg, 1990. (1990) 
  12. Method of Rothe in Evolution Equations, Teubner-Verlag, Leipzig, 1985. (1985) MR0834176
  13. Solution of some free boundary problems by relaxation schemes, Preprint M3-94, Comenius University (Faculty of Mathematics and Physics) in Bratislava, 1994. (1994) MR1664813
  14. Solution to strongly nonlinear parabolic problem by a linear approximation scheme, Preprint M2-96, Comenius University (Faculty of Mathematics and Physics) in Bratislava, 1996. (1996) MR1670689
  15. 10.1137/0730087, SIAM J. Numer. Anal. 30 (1993), 1703–1722. (1993) MR1249039DOI10.1137/0730087
  16. Kapillarer und dampfförmiger Feuchtetransport in mehrschichtlichen Bauteilen, Dissertation, University of Essen, 1983. (1983) 
  17. Die wissenschaftlichen Grundlagen der Trockungstechnik, Springer-Verlag, Berlin, 1978. (1978) 
  18. Feuchtetransport- und Speicherkoeffizienten poröser mineralischer Baustoffen: theoretische Grundlagen und neue Messtechniken, Dissertation, University of Stuttgart, 1995. (1995) 
  19. Function Spaces, Academia, Prague, 1977. (1977) MR0482102
  20. Rechnerische Untersuchungen des Langzeit-Feuchteverhaltens von Wärmedämmschichten in Umkehrdächern mit Begründung, Research report IBP FtB-23, 1993. 
  21. MathWorks MATLAB—The Language of Technical Computing, Application Program Interface Guide, Version 5, The MathWorks, Inc., 1998. (1998) 
  22. Spaces of S. L. Sobolev, Leningrad (St. Petersburg) University Press, 1985. (Russian) (1985) MR0807364
  23. Introduction to the Theory of Nonlinear Elliptic Equations, Teubner-Verlag, Leipzig, 1983. (1983) MR0731261
  24. On the mathematical modelling of the process of the heat and moisture transfer in the porous materials, Research report E11-99-8, Institute of Nuclear Research Dubna (Russia), 1999. (1999) 
  25. Relaxation in Optimization Theory and Variational Calculus, Walter de Gruyter, Berlin, 1997. (1997) MR1458067
  26. 10.1023/A:1022229022563, Appl. Math. 44 (1999), 481–496. (1999) MR1727984DOI10.1023/A:1022229022563
  27. 10.1023/A:1022286318503, Appl. Math. 43 (1998), 351–380. (1998) Zbl1042.74511MR1644132DOI10.1023/A:1022286318503

NotesEmbed ?

top

You must be logged in to post comments.