Global existence for degenerate quadratic reaction-diffusion systems

M. Pierre; R. Texier-Picard

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 5, page 1553-1568
  • ISSN: 0294-1449

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Pierre, M., and Texier-Picard, R.. "Global existence for degenerate quadratic reaction-diffusion systems." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1553-1568. <http://eudml.org/doc/78902>.

@article{Pierre2009,
author = {Pierre, M., Texier-Picard, R.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {atmosphere modelling; one directional diffusion},
language = {eng},
number = {5},
pages = {1553-1568},
publisher = {Elsevier},
title = {Global existence for degenerate quadratic reaction-diffusion systems},
url = {http://eudml.org/doc/78902},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Pierre, M.
AU - Texier-Picard, R.
TI - Global existence for degenerate quadratic reaction-diffusion systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 5
SP - 1553
EP - 1568
LA - eng
KW - atmosphere modelling; one directional diffusion
UR - http://eudml.org/doc/78902
ER -

References

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  1. [1] Bardos C., Problèmes aux limites pour les équations aux dérivées partielles, Ann. Sci. École Norm. Sup. (4)4 (1970) 185-233. Zbl0202.36903MR274925
  2. [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. Zbl0922.47039MR1391154
  3. [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. Zbl1330.35211MR2340282
  4. [4] Fitzgibbon W.E., Langlais M., Morgan J.J., A degenerate reaction–diffusion system modeling atmospheric dispersion of pollutants, J. Math. Anal. Appl. (2005). Zbl1128.35359MR2142434
  5. [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. Zbl0876.35014MR1443610
  6. [6] Ghouali N., Touaoula T.M., A linear model for the dynamics of fish larvae, Electron. J. Differential Equations (140) (2004), 10 p. (electronic). Zbl1070.35500MR2108911
  7. [7] Th. Goudon, A. Vasseur, Regularity analysis for systems of reaction–diffusion equations, in press. Zbl1191.35202
  8. [8] Hörmander L., Hypoelliptic second order differential equations, Acta Math.119 (1967) 147-171. Zbl0156.10701MR222474
  9. [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. [10] Kolmogorov A., Zufällige Bewegungen (zur Theorie der Brownschen Bewegung), Ann. of Math. (2)35 (1) (1934) 116-117, (in German). Zbl0008.39906MR1503147
  11. [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. Zbl1032.35114MR1972000
  12. [12] Langlais M., Solutions fortes pour une classe de problèmes aux limites du second ordre dégénérés, Comm. Partial Differential Equations4 (1979) 869-897. Zbl0438.35032MR537466
  13. [13] Langlais M., A degenerating elliptic problem with unilateral constraints, Nonlinear Anal.4 (1980) 329-342. Zbl0455.35066MR563813
  14. [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. Zbl0174.15403
  15. [15] Martin R.H., Pierre M., Influence of mixed boundary conditions in some reaction–diffusion systems, Proc. Roy. Soc. Edinburgh Sect. A127 (5) (1997) 1053-1066. Zbl0887.35069MR1475645
  16. [16] Morgan J., Global existence for semilinear parabolic systems, SIAM J. Math. Anal.20 (5) (1989) 1128-1144. Zbl0692.35055MR1009350
  17. [17] Oleinik O.A., Radlevic E.V., Second Order Equations with Nonnegative Characteristic Form, Plenum, 1973. MR457908
  18. [18] Pierre M., Weak solutions and supersolutions in L 1 for reaction–diffusion systems, J. Evol. Equ.3 (1) (2003) 153-168. Zbl1026.35047MR1977432
  19. [19] Pierre M., Schmitt D., Blowup in reaction–diffusion systems with dissipation of mass, SIAM Rev.42 (2000) 93-106, (electronic). Zbl0942.35033MR1738101
  20. [20] Rothschild L.P., Stein E.M., Hypoelliptic differential operators on nilpotent groups, Acta Math.137 (1977) 247-320. Zbl0346.35030MR436223
  21. [21] Seinfeld J., Pandis S., Atmospheric Chemistry and Physics, Wiley, New York, 1995. 
  22. [22] Verwer J.G., Hundsdorfer W., Blom J.G., Numerical time integration for air pollution models, Surveys Math. Indust.10 (2002) 107-174. Zbl0999.65097MR1911148

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