Homogenization of transport equations

摘要: This article is devoted to the mathematical analysis of various formulas giving equivalent absorption and scattering cross section for mixed materials in linear transport theory. We begin with a general result on treatment high-frequency oscillations equations which partly based upon velocity averaging results analogue, equations, compensated compactness class results. The case periodic inhomogeneities then studied detail; particular we show essential difference homogenization diffusion due small divisor problems. These were announced [F. Golse, C.R. Acad. Sci. Paris Ser. I Math., 305 (1987), pp. 801--804; F. Mathematical Aspects Fluid Plasma Dynamics, G. Toscani, V. Boffi, S. Rionero, eds., Lecture Notes Math 1460, Springer-Verlag, Berlin, New York, 1991, 152--169]. Finally, treat stochastic theory insp...