A kinetic model for polytropic gases with internal energy. Issue 1 (December 2013)

• Record Type: Journal Article
• Authors: Boudin, Laurent; Grec, Bérénice; Pavić‐Čolić, Milana; Salvarani, Francesco
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 13:Issue 1(2013)
• Page Start: 353
• Page End: 354
• Publication Date: 2013-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201310172
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We consider a mixture of <italic>N</italic> ideal, polytropic gases. Each species is described by a distribution function <italic>f_{<italic>i</italic>}(t, x, v, I) ≥ 0, 1 ≤ i ≤ N</italic>, defined on <tex-math notation="tex"><![CDATA[${\rm I\!R}_+\times{\rm I\!R}^3\times{\rm I\!R}^3\times{\rm I\!R}_+$]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg3z40cp5q" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />, and its evolution is governed by a Boltzmann‐type equation. In order to recover the energy law of polytropic gases, the authors of [4] proposed a kinetic model in the framework of a weighted <italic>L</italic>¹ space. Another approach has been developed in [3] in the context of polyatomic gases. Following this previous lead, our model provides a <italic>L</italic>² framework in both variables <italic>v</italic> and <italic>I</italic>, to eventually perform a mathematical study of the diffusion asymptotics, as it was done in [2] for a model without energy exchange. (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>