Stability estimates on general scalar balance laws

Rinaldo M. Colombo; Magali Mercier; Massimiliano D. Rosini

doi:10.1016/j.crma.2008.11.005

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. Colombo ¹ ; Magali Mercier ¹ ; Massimiliano D. Rosini ¹

¹ Department of Mathematics, Brescia University, Via Branze 38, 25133 Brescia, Italy

Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 45-48.

Résumé
Abstract

Nous considérons ici une loi de conservation généralisée en dimension N : $\partial_{t} u + Div f (t, x, u) = F (t, x, u)$ . 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 $\partial_{t} u + Div f (t, x, u) = F (t, x, u)$ . 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 : 2008-07-14
Accepté le : 2008-10-29
Publié le : 2008-11-26

DOI : 10.1016/j.crma.2008.11.005

Affiliations des auteurs :

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},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {45--48},
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     year = {2009},
     doi = {10.1016/j.crma.2008.11.005},
     language = {en},
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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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