Diffusion limit for the radiative transfer equation perturbed by a Markovian process

Article type: Research Article

Authors: Debussche, A.^{a; *} | De Moor, S.^a | Vovelle, J.^b

Affiliations: [a] IRMAR, ENS Rennes, CNRS, UEB. av Robert Schuman, F-35170 Bruz, France. E-mails: arnaud.debussche@ens-rennes.fr, sylvain.demoor@ens-rennes.fr | [b] Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, F-69622 Villeurbane Cedex, France. E-mail: vovelle@math.univ-lyon1.fr

Correspondence: [*] Corresponding author. E-mail: arnaud.debussche@ens-rennes.fr.

Abstract: We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non linear, involving a small parameter and perturbed by a smooth random term. Under an appropriate scaling for the small parameter, using a generalization of the perturbed test-functions method, we show the convergence in law to a stochastic non linear fluid limit.

Keywords: kinetic equations, non-linear, diffusion limit, stochastic partial differential equations, perturbed test functions, Rosseland approximation, radiative transfer

DOI: 10.3233/ASY-161360

Journal: Asymptotic Analysis, vol. 98, no. 1-2, pp. 31-58, 2016