dc.contributor.author Dalibard, Anne-Laure dc.date.accessioned 2014-05-19T08:44:39Z dc.date.available 2014-05-19T08:44:39Z dc.date.issued 2007 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/13320 dc.language.iso en en dc.subject homogenization en dc.subject kinetic formulation en dc.subject scalar conservation law en dc.subject.ddc 515 en dc.title Kinetic Formulation for a Parabolic Conservation Law. Application to Homogenization en dc.type Article accepté pour publication ou publié dc.description.abstracten We 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.isversionofjnlname SIAM Journal on Mathematical Analysis dc.relation.isversionofjnlvol 39 en dc.relation.isversionofjnlissue 3 en dc.relation.isversionofjnldate 2007 dc.relation.isversionofjnlpages 891-915 en dc.relation.isversionofdoi http://dx.doi.org/10.1137/060662770 en dc.relation.isversionofjnlpublisher SIAM en dc.subject.ddclabel Analyse en dc.relation.forthcoming non en dc.relation.forthcomingprint non en
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