Global Existence for Degenerate Quadratic Reaction-Diffusion Systems
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1553-1568.
@article{AIHPC_2009__26_5_1553_0,
     author = {Pierre, M. and Texier-Picard, R.},
     title = {Global {Existence} for {Degenerate} {Quadratic} {Reaction-Diffusion} {Systems}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1553--1568},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.06.003},
     mrnumber = {2566699},
     zbl = {1180.35288},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.06.003/}
}
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Pierre, M.; Texier-Picard, R. Global Existence for Degenerate Quadratic Reaction-Diffusion Systems. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1553-1568. doi : 10.1016/j.anihpc.2008.06.003. http://www.numdam.org/articles/10.1016/j.anihpc.2008.06.003/

[1] Bardos C., Problèmes Aux Limites Pour Les Équations Aux Dérivées Partielles, Ann. Sci. École Norm. Sup. (4) 4 (1970) 185-233. | EuDML | Numdam | MR | Zbl

[2] Bramanti M., Cerutti M. C., Manfredini M., L p Estimates for Some Ultraparabolic Operators With Discontinuous Coefficients, J. Math. Anal. Appl. 200 (1996) 332-354. | MR | Zbl

[3] Desvillettes L., Fellner K., Pierre M., Vovelle J., About Global Existence for Quadratic Systems of Reaction-Diffusion, Adv. Nonlinear Stud. 7 (3) (2007) 491-511. | MR | Zbl

[4] Fitzgibbon W. E., Langlais M., Morgan J. J., A Degenerate Reaction-Diffusion System Modeling Atmospheric Dispersion of Pollutants, J. Math. Anal. Appl. (2005). | MR | Zbl

[5] Fitzgibbon W. E., Hollis S. L., Morgan J. J., Stability and Lyapunov Functions for Reaction-Diffusion Systems, SIAM J. Math. Anal. 28 (3) (1997) 595-610. | MR | Zbl

[6] Ghouali N., Touaoula T. M., A Linear Model for the Dynamics of Fish Larvae, Electron. J. Differential Equations (140) (2004), 10 p. (electronic). | EuDML | MR | Zbl

[7] Th. Goudon, A. Vasseur, Regularity analysis for systems of reaction-diffusion equations, in press.

[8] Hörmander L., Hypoelliptic Second Order Differential Equations, Acta Math. 119 (1967) 147-171. | MR | Zbl

[9] Kim J., Cho S., Computation Accuracy and Efficiency of the Time Splitting Method in Solving Atmospheric Transport Equations, Atmos. Environ. 31 (1997) 2215-2224.

[10] Kolmogorov A., Zufällige Bewegungen (Zur Theorie Der Brownschen Bewegung), Ann. of Math. (2) 35 (1) (1934) 116-117, (in German). | MR | Zbl

[11] Lanconelli E., Pascucci A., Polidoro S., Linear and Nonlinear Ultraparabolic Equations of Kolmogorov Type Arising in Diffusion Theory and in Finance, in: Nonlinear Problems in Mathematical Physics and Related Topics, II, Int. Math. Ser. (N.Y.), vol. 2, Kluwer/Plenum, New York, 2002, pp. 243-265. | MR | Zbl

[12] Langlais M., Solutions Fortes Pour Une Classe De Problèmes Aux Limites Du Second Ordre Dégénérés, Comm. Partial Differential Equations 4 (1979) 869-897. | MR | Zbl

[13] Langlais M., A Degenerating Elliptic Problem With Unilateral Constraints, Nonlinear Anal. 4 (1980) 329-342. | MR | Zbl

[14] Ladyzenskaya O. A., Solonnikov V. A., Uralceva N. N., Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968. | Zbl

[15] Martin R. H., Pierre M., Influence of Mixed Boundary Conditions in Some Reaction-Diffusion Systems, Proc. Roy. Soc. Edinburgh Sect. A 127 (5) (1997) 1053-1066. | MR | Zbl

[16] Morgan J., Global Existence for Semilinear Parabolic Systems, SIAM J. Math. Anal. 20 (5) (1989) 1128-1144. | MR | Zbl

[17] Oleinik O. A., Radlevic E. V., Second Order Equations With Nonnegative Characteristic Form, Plenum, 1973. | MR

[18] Pierre M., Weak Solutions and Supersolutions in L 1 for Reaction-Diffusion Systems, J. Evol. Equ. 3 (1) (2003) 153-168. | MR | Zbl

[19] Pierre M., Schmitt D., Blowup in Reaction-Diffusion Systems With Dissipation of Mass, SIAM Rev. 42 (2000) 93-106, (electronic). | MR | Zbl

[20] Rothschild L. P., Stein E. M., Hypoelliptic Differential Operators on Nilpotent Groups, Acta Math. 137 (1977) 247-320. | MR | Zbl

[21] Seinfeld J., Pandis S., Atmospheric Chemistry and Physics, Wiley, New York, 1995.

[22] Verwer J. G., Hundsdorfer W., Blom J. G., Numerical Time Integration for Air Pollution Models, Surveys Math. Indust. 10 (2002) 107-174. | MR | Zbl

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