Asymptotic analysis of an advection-diffusion equation and application to boundary controllability

Article type: Research Article

Authors: Amirat, Youcef | Münch, Arnaud^{; *}

Affiliations: Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne, UMR CNRS 6620, Campus universitaire des Cézeaux, 3, place Vasarely, 63178, Aubière, France. E-mails: youcef.amirat@uca.fr, arnaud.munch@uca.fr

Correspondence: [*] Corresponding author. E-mail: arnaud.munch@uca.fr.

Abstract: We perform the asymptotic analysis of the scalar advection-diffusion equation ytε−εyxxε+Myxε=0, (x,t)∈(0,1)×(0,T), M>0, with respect to the diffusion coefficient ε. We use the matched asymptotic expansion method which allows to describe the boundary layers of the solution. We then use the asymptotics to discuss the controllability property of the solution for T⩾1/M.

Keywords: Asymptotic analysis, boundary layers, singular controllability

DOI: 10.3233/ASY-181497

Journal: Asymptotic Analysis, vol. 112, no. 1-2, pp. 59-106, 2019