Homogenization in the energy variable for a neutron transport model

Article type: Research Article

Authors: Hutridurga, Harsha^{a; *} | Mula, Olga^b | Salvarani, Francesco^{b; c}

Affiliations: [a] Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India. E-mail: hutri@math.iitb.ac.in | [b] Université Paris-Dauphine, PSL University, CNRS, UMR 7534, CEREMADE, 75016 Paris, France. E-mail: mula@ceremade.dauphine.fr | [c] Università degli Studi di Pavia, Dipartimento di Matematica, I-27100 Pavia, Italy. E-mail: francesco.salvarani@unipv.it

Correspondence: [*] Corresponding author. E-mail: hutri@math.iitb.ac.in.

Abstract: This article addresses the homogenization of linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit. We also provide some numerical experiments to illustrate our results. In the Appendix, we treat a related case of the harmonic oscillator.

Keywords: Linear Boltzmann equation, self-shielding, two-scale convergence, memory effects

DOI: 10.3233/ASY-191544

Journal: Asymptotic Analysis, vol. 117, no. 1-2, pp. 1-25, 2020