Comptes Rendus
no. 1-2
Partial Differential Equations
Stability estimates on general scalar balance laws
[Estimation de la variation totale et stabilité pour des lois de conservations scalaires généralisées]

Présenté par : Jean-Michel Bony

Rinaldo M. Colombo1 ; Magali Mercier1 ; Massimiliano D. Rosini1
1 Department of Mathematics, Brescia University, Via Branze 38, 25133 Brescia, Italy
Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 45-48.

Nous considérons ici une loi de conservation généralisée en dimension N : ∂tu+Divf(t,x,u)=F(t,x,u). Sous des hypothèses adaptées pour f et F, nous obtenons une borne de la variation totale de la solution. À partir de ce résultat, il est alors possible de donner une estimation de la dépendance des solutions au flot f et au terme source F. Dans les cas particuliers déjà étudiés, notre résultat se réduit à ceux déjà connus.

Consider the general scalar balance law in N space dimensions ∂tu+Divf(t,x,u)=F(t,x,u). Under suitable assumptions on f and F, we provide bounds on the total variation of the solution. Based on this first result, we establish estimates on the dependence of the solutions from f and F. In the more particular cases considered in the literature, the present estimate reduces to the known ones.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.11.005
Rinaldo M. Colombo 1 ; Magali Mercier 1 ; Massimiliano D. Rosini 1

1 Department of Mathematics, Brescia University, Via Branze 38, 25133 Brescia, Italy 
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     title = {Stability estimates on general scalar balance laws},
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Rinaldo M. Colombo; Magali Mercier; Massimiliano D. Rosini. Stability estimates on general scalar balance laws. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 45-48. doi : 10.1016/j.crma.2008.11.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.005/

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[5] R.M. Colombo, M. Mercier, M.D. Rosini, Stability and total variation estimates on general scalar balance laws, Comm. Math. Sci., submitted for publication

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