On the stability of a forward-backward heat equation

2011/10/31 by Lyonell Boulton, Marco Marletta, Boulton, Lyonell +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.1110.6869

21 pages, 3 figures

arxiv created 2011/10/31 · arxiv updated 2011/11/01

Abstract

In this paper we examine spectral properties of a family of periodic singular Sturm-Liouville problems which are highly non-self-adjoint but have purely real spectrum. The problem originated from the study of the lubrication approximation of a viscous fluid film in the inner surface of a rotating cylinder and has received a substantial amount of attention in recent years. Our main focus will be the determination of Schatten class inclusions for the resolvent operator and regularity properties of the associated evolution equation.

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