On the singular limit of a model transport semigroup
Mustapha Mokhtar‐Kharroubi, V. Protopopescu, L. Thevenot · Mathematical Methods in the Applied Sciences · 2000
We consider the diffusion limit of a model transport equation on the torus or the whole space, as a scaling parameter ε (the mean free path), tends to zero. We show that, for arbitrary initial data $u_0(x,v)$ opagenumbers\end , the solution converges in norm topology for each $t>0$ opagenumbers\end , to the solution of a diffusion equation with initial data \def\d{{\rm d}}$u_D^0(x)=\int u_0(x,v)\,\d v$ opagenumbers\end. The proof relies on Fourier analysis which diagonalizes the transport operator, a Dunford functional calculus and the analysis of the behaviour of the transport spectrum as ε tends to zero. Copyright © 2000 John Wiley & Sons, Ltd.