PUMA
Istituto di Matematica Applicata e Tecnologie Informatiche     
Sangalli G. Analysis of the advection-diffusion operator using fractional order norms. Preprint ercim.cnr.ian//2001-1221, 2001.
 
 
Abstract
(English)
In this paper we obtain a family of optimal estimates for the linear advection-diffusion operator. More precisely we define norms on its domain and, accordingly, norms on its image, such that it behaves as an isomorphism: it remains bounded as well as its inverse does, uniformly with respect to the diffusion parameter. The analysis makes use of interpolation between functional spaces. One motivation of this work is our interest in the theoretical properties of stable numerical methods for this kind of problems: we only give here some hints and postpone deeper investigations to a further paper.
Subject Advection-diffusion
76M10, 46B70


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