Bernard Brighi

 

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Publications parues ou à paraître

[1] B. Brighi et M. Chipot : Densités d'énergie et matériaux cristallins. Annales de la Faculté des Sciences de Toulouse, Série 6, Vol. 1, No. 1 (1992) 15-24.

 

[2] B. Brighi et M. Chipot : Approximation in nonconvex problems. Progress in partial differential equations : calculus of variations, applications. C. Bandle, J. Bemelmans, M. Chipot, M. Grüter and J. Saint Jean Paulin, eds., Pitman Research Notes in Mathematics Series # 267, Longman Scientific & Technical, 1992.

 

[3] B. Brighi et M. Chipot : Approximated convex envelope of a function. S.I.A.M. Journal on Numerical Analysis. Vol. 31, No. 1 (1994) 128-148.

 

[4] B. Brighi : Sur l'enveloppe convexe d'une fonction de la variable réelle. Revue de Mathématiques Spéciales, Vuibert, 104ème année, No. 8 (1994) 547-550.

 

[5] B. Brighi et M. Bousselsal : On the rank-one-convexity domain of the Saint Venant-Kirchhof stored energy function. Rendiconti del Seminario Matematico dell'Università di Padova. Vol. 94, No. 4 (1995) 25-45.

 

[6] B. Brighi et G. Vergara Caffarelli : The existence of stationary solution for a balance equation in structured continua. Istituto per le Applicazioni del Calcolo "Mauro Picone" Consiglio Nazionale delle Ricerche, Quaderno n. 14, Rome, 1996.

 

[7] M. Bousselsal et B. Brighi : Rank-one-convex and quasiconvex envelopes for functions depending on quadratic forms. Journal of Convex Analysis. Vol. 4, No. 2 (1997) 303-318.

 

[8] B. Brighi, M. Chipot et E. Gut : Finite differences on triangular grids. Numer Methods Partial Differential Eq Vol. 14 (1998) 567-579.

 

[9] B. Brighi et M. Chipot : Approximation of Infima in the Calculus of Variations. Journal of Computational and Applied Mathematics 98 (1998) 273-287.

 

[10] B. Brighi et M. Ramaswamy : On some general semilinear elliptic problems with nonlinear boundary conditions. Advances in Differential Equations. Vol. 4, No. 3 (1999) 369-390.

 

[11] Z. Belhachmi, B. Brighi et K. Taous : Solutions similaires pour un problèmes de couches limites en milieux poreux. C. R. Acad. Sci. Paris, t. 328, Série II, b (2000) 407-410.

 

[12] Z. Belhachmi, B. Brighi et K. Taous : On the concave solutions of the Blasius equation. Acta Math. Univ. Comenianae, Vol. 69, No. 2 (2000) 199-214. 

 

[13] B. Brighi : Deux problèmes aux limites pour l'équation de Blasius. Revue des mathématiques de l'enseignement supérieur (RMS), Vuibert, 111ème année, No. 8 (2001) 833-842.

 

[14] Z. Belhachmi, B. Brighi et K. Taous : On a family of differential equations for boundary layer approximations in porous media. Euro. Jnl of Applied Mathematics, Vol. 12 (2001) 513-528. 

 

[15] B. Brighi : On a similarity boundary layer equation. Zeitschrift für Analysis und ihre Anwendungen, Vol. 21, No. 2 (2002) 931-948. 

 

[16] Z. Belhachmi, B. Brighi, J.M. Sac Epée et K. Taous : Numerical simulations of free convection about vertical flat plate embedded in porous media. Computational Geosciences 7 (2003), 137-166.

 

[17] B. Brighi et T. Sari : Blowing-up coordinates for a similarity boundary layer equation. Discrete and Continuous Dynamical Systems, Vol. 12, No. 5 (2005) 929-948.

 

[18] B. Brighi et J.-D. Hoernel : On similarity solutions for boundary layer flows with prescribed heat flux. Mathematical Methods in the Applied Sciences, Vol. 28, No. 4 (2005) 479-503. 

 

[19] B. Brighi et J.-D. Hoernel : On the concave and convex solutions of mixed convection boundary layer approximation in a porous medium. Applied Mathematics Letters, Vol. 19, No. 1 (2006) 69-74. 

 

[20] B. Brighi et J.-D. Hoernel : Asymptotic behavior of the unbounded solutions of some boundary layer equations. Archiv der Mathematik, Vol. 85, No. 2 (2005) 161-166. 

 

[21] B. Brighi et J.-D. Hoernel : Recent advances on similarity solutions arising during free convection. Progress in Nonlinear Differential Equations and Their Applications, Vol. 63, pp. 83-92, Birkhäuser Verlag Basel/Switzerland, 2005.

 

[22] S. Akesbi, B. Brighi et J.-D. Hoernel : Steady free convection in a bounded and saturated porous medium. Proceedings of the Swiss-Japanese Seminar on Elliptic and Parabolic Issues in Applied Sciences, Zürich, December 2004, pp. 1-17. World Scientific Publishing Co. Pte. Ltd., 2006.

 

[23] B. Brighi et J.-D. Hoernel : Similarity solutions for high frequency excitation of liquid metal in an antisymmetric field. Self-similar solutions of nonlinear PDE, Banach Center Publications, Vol. 74,(2006) 41-57. 


[24] B. Brighi et S. Guesmia : Asymptotic behavior of solution of hyperbolic problems on a cylindrical domain. Discrete and Continuous Dynamical Systems, Supplements (2007) 160-169. 


[25] B. Brighi et J.-D. Hoernel : On a general similarity boundary layer equation. Acta Math. Univ. Comenianae, Vol. 77, No. 1 (2008) 9-22.


[26] B. Brighi et S. Guesmia : On a nonlinear system of PDE's arising in free convection. Proceeding of the Ryukoku Workshop 2007 ``Recent Advances on Nonlinear Parabolic and Elliptic Differential Equations'', Y. Morita, H. Ninomiya, E. Yanagida, eds. (2008) 35-43.


[27] B. Brighi, A. Fruchard et T. Sari : On the Blasius problem. Adv. Differential Equations, Vol. 13, No. 5-6 (2008) 509-600.


[28] B. Brighi et S. Guesmia : On elliptic boundary value problems of order 2m in cylindrical domain of large size. Adv. Math. Sci. Appl. Vol. 18 (2008) 237-250.


[29] B. Brighi et N. Chevallier : 1n2+cos n = +. Revue de la filière Mathématique (RMS), Vol. 119, No. 1 (2008-2009) 3-8. 


[30] B. Brighi et S. Guesmia : Existence of solutions and iterative approximations for nonlinear systems arising in free convection. Analysis and Applications, Vol. 7, No. 3 (2009) 225-241.


[31] M. Aïboudi et B. Brighi : On the solutions of a boundary value problem arising in free convection with prescribed heat flux. Archiv der Mathematik, Vol. 93, No. 2 (2009) 165-174.


Articles soumis ou en préparation


[32] B. Brighi : Sur un problème aux limites associé à l'équation différentielle  f ''' + f f '' + 2 f ' 2 = 0.


[33] B. Brighi : On the differential equation  f ''' + f f '' + g(f ') = 0  and the associated boundary value problems.