On the singular limit of a model transport semigroup

✍ Scribed by M. Mokhtar-Kharroubi; V. Protopopescu; L. Thevenot

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 182 KB
• Volume: 23
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/1099-1476(200010)23:15<1301::aid-mma166>3.0.co;2-6

✦ Synopsis

We consider the di!usion limit of a model transport equation on the torus or the whole space, as a scaling parameter (the mean free path), tends to zero. We show that, for arbitrary initial data u (x, v), the solution converges in norm topology for each t'0, to the solution of a di!usion equation with initial data u " (x)" u (x, v) dv. 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 tends to zero.