Asymptotics of the Spectrum of an Integro-Differential Equation Arising in the Study of the Flutter of a Viscoelastic Plate

In the paper, the asymptotics for the spectrum of the symbol of the oscillation equation of a viscoelastic plate in a liquid or gas flow is studied using operator analysis methods. This equation is the Gurtin–Pipkin equation with a relatively compact perturbation. Using an operator analog of Rouche’s theorem, we explicitly define an asymptotic representation of nonreal points of the spectrum for the symbol of the equation. DOI 10.1134/S1061920821020059