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Kinetic Formulation for a Parabolic Conservation Law. Application to Homogenization

dc.contributor.authorDalibard, Anne-Laure
dc.date.accessioned2014-05-19T08:44:39Z
dc.date.available2014-05-19T08:44:39Z
dc.date.issued2007
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13320
dc.language.isoenen
dc.subjecthomogenizationen
dc.subjectkinetic formulationen
dc.subjectscalar conservation lawen
dc.subject.ddc515en
dc.titleKinetic Formulation for a Parabolic Conservation Law. Application to Homogenizationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe derive a kinetic formulation for the parabolic scalar conservation law $\partial_t u + \mathrm{div}_y A(y,u) - \Delta_y u=0$. This allows us to define a weaker notion of solutions in $L^1$, which is enough to recover the $L^1$ contraction principle. We also apply this kinetic formulation to a homogenization problem studied in a previous paper; namely, we prove that the kinetic solution $u^{\varepsilon}$ of $\partial_t u^{\varepsilon} + \mathrm{div}_x A\left({x}/{\varepsilon}, u^{\varepsilon} \right)- \varepsilon\Delta_x u^{\varepsilon}=0$ behaves in $L^1_{\text{loc}}$ as $v\left( {x}/{\varepsilon}, \bar{u}(t,x)\right)$, where v is the solution of a cell problem and $\bar{u}$ the solution of the homogenized problem.en
dc.relation.isversionofjnlnameSIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol39en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2007
dc.relation.isversionofjnlpages891-915en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/060662770en
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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