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Compétition Réaction-Diffusion et comportement asymptotique d’un problème d’obstacle doublement non linéaire
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 2, pp. 345-362.

Le but de cet article est l’étude de la compétition Réaction-Diffusion pour un problème de type β(w) t -d ε diva(x,Dw)+r ε gx , β ( w )=f,a est un opérateur de Lerray-Lions, β est une fonction continue croissante et la réaction g est une fonction croissante qui dépend de l’espace x. On suppose que les coefficients de diffusion d ε et de Réaction r ε dépendent du paramètre ε avec d ε et/ou r ε tends vers + lorsque ε0. Dans le cas où, le coefficient de réaction est très rapide, nous étudions le comportement asymptotique lorsque t de la solution du problème d’obstacle afin de caractériser la donnée initiale du problème limite.

In this paper, we study the competition between the diffusion and the reaction for the problem of type β(w) t -d ε diva(x,Dw)+r ε gx , β ( w )=f, where a is a Lerray-Lions operator, β is a nondecreasing continuous function and the reaction g is a nondecreasing function that depend on the space x. Assume that, the coefficient of diffusion d ε and the reaction r ε depend on the parameter ε with d ε and/or r ε tends to + as ε0. In the case when, the reaction coefficient is very fast, we study the asymptotic behavior as t of the solution of the obstacle problem to characterize the initial data for the limit problem.

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DOI : https://doi.org/10.5802/afst.1246
@article{AFST_2010_6_19_2_345_0,
     author = {Fahd Karami},
     title = {Comp\'etition {R\'eaction-Diffusion} et comportement asymptotique d{\textquoteright}un probl\`eme d{\textquoteright}obstacle doublement non lin\'eaire},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {345--362},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 19},
     number = {2},
     year = {2010},
     doi = {10.5802/afst.1246},
     zbl = {1203.35147},
     mrnumber = {2674766},
     language = {fr},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1246/}
}
Fahd Karami. Compétition Réaction-Diffusion et comportement asymptotique d’un problème d’obstacle doublement non linéaire. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 2, pp. 345-362. doi : 10.5802/afst.1246. https://afst.centre-mersenne.org/articles/10.5802/afst.1246/

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