@article{AMBP_2001__8_2_1_0, author = {N. Alaa and I. Mounir}, title = {Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {1--19}, publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal}, volume = {8}, number = {2}, year = {2001}, zbl = {01805809}, mrnumber = {1888813}, language = {en}, url = {https://ambp.centre-mersenne.org/item/AMBP_2001__8_2_1_0/} }
TY - JOUR AU - N. Alaa AU - I. Mounir TI - Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient JO - Annales mathématiques Blaise Pascal PY - 2001 SP - 1 EP - 19 VL - 8 IS - 2 PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal UR - https://ambp.centre-mersenne.org/item/AMBP_2001__8_2_1_0/ LA - en ID - AMBP_2001__8_2_1_0 ER -
%0 Journal Article %A N. Alaa %A I. Mounir %T Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient %J Annales mathématiques Blaise Pascal %D 2001 %P 1-19 %V 8 %N 2 %I Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal %U https://ambp.centre-mersenne.org/item/AMBP_2001__8_2_1_0/ %G en %F AMBP_2001__8_2_1_0
N. Alaa; I. Mounir. Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient. Annales mathématiques Blaise Pascal, Tome 8 (2001) no. 2, pp. 1-19. https://ambp.centre-mersenne.org/item/AMBP_2001__8_2_1_0/
[1] solutions faibles d'équations paraboliques quasi-linéaires avec données initiales mesures. Ann. Math. Blaise Pascal, 3 N°2, pp. 1 - 15(1996). | Numdam | MR | Zbl
,[2] Global existence for reaction-diffusion systems with mass control and critical growth with respect to the gradient. Journal of Mathematical Analysis and Applications 253, pp.532 - 557, (2001). | MR | Zbl
, ,[3] Weak solutions for some quasilinear elliptic equations with data measures. SIAM J. Math. Anal, vol 24, n°1, p. 23 - 35, (1993). | MR | Zbl
, .[4] On a non linear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. Henri Poincaré. vol 5, n°4,p. 347 - 364(1988). | Numdam | MR | Zbl
, and ,[5] Existence results for some quasilinear parabolic equations, Nonlinear Anlysis. Theory. Methods & Applications, 13, N° 4, pp. 373 - 392(1989). | MR | Zbl
, , ,[6] Strongly nonlinear elliptic equations having natural growth terms in L1 data. Nonlinear Anal. T.M.A., vol 19, pp. 573 - 579, (1992). | MR | Zbl
, .[7] Existence de solutions faibles des équations elliptiques quasi-lineaires à croissance quadratique. Nonlinear P.D.E. and their applications, Collège de France Seminar, Vol IV, ed. by H. Brezis& J. L. Lions. Research Notes in Mathematics 84, Pitman, London, pp. 19 - 73, (1983). | MR | Zbl
, , .[8] Semi-linear elliptic equation in L1, J. Math. Soc. Japan, Vol. 25, pp; 565 - 590(1973). | MR | Zbl
, ,[9] Global existence and boundedness for class of inhomogeneous semilinear parabolic systems, Nonlinear Analysis, Theory Methods and Applications, Vol. 19,N°9,pp.885-899(1992). | MR | Zbl
, , .[10] Global Existence and Boundeness in Reaction-Diffusion Systems, SIAM. J. Math. Anal. 18, pp. 744 - 761, (1987). | MR | Zbl
, , ,[11] quelques méthodes de résolutions des problèmes aux limites non linéaires, Dunod-Gauthier Villars(1969). | MR | Zbl
,[12] Existence pour des systèmes de réaction-diffusion quasi-lineaires avec loi de balance. Thèse de Doctorat de l'Université Henri Poincaré, Nancy I, (1994).
.[13] Nonlinear reaction-diffusion systems, in "Nonlinear Equations in the Applied Sciences", ed W. F. Ames, C. Rogers and Kapell, Academic Press (1991), Notes and reports in Mathematics in Science and Engineering.
, ,[14] An L1 method to prove global existence in some reaction-diffusion systems, in Contributions to nonlinear partial differential equations,J. I. Lionset P. L. Lions Pitman Res. Notes in Math. Series, pp. 220 - 231(1987). | MR | Zbl
,[15] Existence for elliptic equations in L1 having lower order terms with natural growth.Portugaliae Mathematica Vol. 57 Fasc.2 - 2000. | MR | Zbl
.[16] Global Solutions of Reaction-Diffusion Systems, Lectures Notes in Math. 1072, Springer-Verlag (1984). | MR | Zbl
,[17] Shock waves and reaction-diffusion equations, in Comprehensive Studies in Mathematics, Vol. 258. Springer, New York (1984). | Zbl
.