On the stability of a forward-backward heat equation

Lyonell Boulton; Marco Marletta; David Rule

doi:10.1007/s00020-012-1963-y

On the stability of a forward-backward heat equation

Lyonell Boulton^*, Marco Marletta, David Rule

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	195-216
Number of pages	22
Journal	Integral Equations and Operator Theory
Volume	73
Issue number	2
DOIs	https://doi.org/10.1007/s00020-012-1963-y
Publication status	Published - 1 Jun 2012

Keywords

NONSELF-ADJOINT OPERATOR
EIGENVALUES
SPECTRUM

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10.1007/s00020-012-1963-y

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AU - Marletta, Marco

AU - Rule, David

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N2 - 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.

AB - 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.

KW - NONSELF-ADJOINT OPERATOR

KW - EIGENVALUES

KW - SPECTRUM

U2 - 10.1007/s00020-012-1963-y

DO - 10.1007/s00020-012-1963-y

M3 - Article

SN - 0378-620X

VL - 73

SP - 195

EP - 216

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

On the stability of a forward-backward heat equation

Abstract

Keywords

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