General minimum principles for quasilinear transport and bioheat equations

Józef Joachim Telega; Maciej Stańczyk

doi:10.1016/j.crme.2004.02.012

General minimum principles for quasilinear transport and bioheat equations

Presented by: Évariste Sanchez-Palencia

Józef Joachim Telega ¹; Maciej Stańczyk ¹

¹ Polish Academy of Sciences, Institute of Fundamental Technological Research, 00-049 Warsaw, Poland

Comptes Rendus. Mécanique, Volume 332 (2004) no. 4, pp. 263-269.

Abstract
Résumé

The aim of this contribution is to derive minimum principles for quasi-linear linear transport (heat) equations in the steady and nonstationary case. Application to currently used nonstationary bioheat equations is sketched.

Le but de la contribution est de donner des principes de minimum pour l'equation du transport (de la chaleur) quasi lineéaire dans le cas stationaire et non stationaire. L'application aux équations de la chaleur, couramment utilisées en biomécanique est esquisée.

Received: 2003-10-20
Accepted: 2004-01-27
Published online: 2004-03-16

DOI: 10.1016/j.crme.2004.02.012

Keywords: Heat transfer, Biomechanics, Quasilinear transport equations, Steady and nonstationary case, Bioheat equations, Minimum principles
Mots-clés : Transferts thermiques, Biomécanique, Cas stationnaire et non stationnaire, Principes de minimum, Equations de la chaleur en biomécanique

Author's affiliations:

Józef Joachim Telega ¹; Maciej Stańczyk ¹

¹ Polish Academy of Sciences, Institute of Fundamental Technological Research, 00-049 Warsaw, Poland

@article{CRMECA_2004__332_4_263_0,
     author = {J\'ozef Joachim Telega and Maciej Sta\'nczyk},
     title = {General minimum principles for quasilinear transport and bioheat equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {263--269},
     publisher = {Elsevier},
     volume = {332},
     number = {4},
     year = {2004},
     doi = {10.1016/j.crme.2004.02.012},
     language = {en},
}

TY  - JOUR
AU  - Józef Joachim Telega
AU  - Maciej Stańczyk
TI  - General minimum principles for quasilinear transport and bioheat equations
JO  - Comptes Rendus. Mécanique
PY  - 2004
SP  - 263
EP  - 269
VL  - 332
IS  - 4
PB  - Elsevier
DO  - 10.1016/j.crme.2004.02.012
LA  - en
ID  - CRMECA_2004__332_4_263_0
ER  -

%0 Journal Article
%A Józef Joachim Telega
%A Maciej Stańczyk
%T General minimum principles for quasilinear transport and bioheat equations
%J Comptes Rendus. Mécanique
%D 2004
%P 263-269
%V 332
%N 4
%I Elsevier
%R 10.1016/j.crme.2004.02.012
%G en
%F CRMECA_2004__332_4_263_0

Józef Joachim Telega; Maciej Stańczyk. General minimum principles for quasilinear transport and bioheat equations. Comptes Rendus. Mécanique, Volume 332 (2004) no. 4, pp. 263-269. doi : 10.1016/j.crme.2004.02.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.02.012/

References
Cited by

[1] H. Brezis; I. Ekeland Un principe variationel associé à certaines équations paraboliques. Le cas indépendant du temps, C. R. Acad. Sci. Paris, Sér. A, Volume 282 (1976), pp. 971-974

[2] H. Brezis; I. Ekeland Un principe variationel associé à certaines équations paraboliques. Le cas dépendant du temps, C. R. Acad. Sci. Paris, Sér. A, Volume 282 (1976), pp. 1197-1198

[3] G. Auchmuty Variational principles for operator equations and initial value problems, Nonlinear Anal., Volume 12 (1988), pp. 531-564

[4] J.J. Telega Extremum principles for nonpotential and initial-value problems, Arch. Mech., Volume 54 (2002), pp. 663-690

[5] J. Ekeland; R. Temam Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976

[6] A. Gałka; J.J. Telega; S. Tokarzewski Nonlinear transport equation and macroscopic properties of microheterogeneous media, Arch. Mech., Volume 49 (1997), pp. 293-319

[7] R.T. Rockafellar; R.J.-B. Wets Variational Analysis, Springer, Berlin, 1998

[8] M. Stańczyk, Modelling of PMMA cement polymerisation, J. Biomech. (2004), in press

[9] M. Stańczyk; J.J. Telega Modelling of heat transfer in biomechanics – a review. Part I. Soft tissues, Acta Bioeng. Biomech., Volume 4 (2002), pp. 31-61

[10] H.H. Pennes Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol., Volume 1 (1948), pp. 93-122

[11] E.H. Wissler Pennes' 1948 paper revisited, J. Appl. Physiol., Volume 85 (1998), pp. 35-41

[12] W. Wulff The energy conservation equation for living tissue, IEEE Trans. Biomed. Engrg., Volume 21 (1974), pp. 494-495

[13] S. Weinbaum; L. Jiji A new simplified bioheat equation for the effect of the local blood flow on local average tissue temperature, J. Biomech. Engrg., Volume 107 (1985), pp. 131-139

[14] F. Bardati; G. Gerosa On the solution of the nonlinear bioheat equation, J. Biomech., Volume 23 (1990), pp. 791-798

[15] M. Stańczyk; J.J. Telega Thermal problems in artificial joints: influence of bone cement polymerisation, Acta Bioeng. Biomech., Volume 3 (2001), pp. 489-496

[16] M. Stańczyk; J.J. Telega Modelling of heat transfer phenomena during cementation of femoral prosthesis, Acta Bioeng. Biomech., Volume 4 (2002), pp. 247-248

Cited by Sources:

Comments - Policy