Spectral properties of a class of operator functions with applications to the Moore-Gibson-Thompson equation with memory

Abstract

In this study, we present spectral enclosures and accumulation of eigenvalues of a class of operator functions with several unbounded operator coefficients. Our findings have direct relevance to the third-order Moore-Gibson-Thompson equation with memory and additional damping. The new results include sufficient conditions for the accumulation of branches of eigenvalues to the essential spectrum and new spectral enclosures for operator functions with several unbounded operator coefficients. To illustrate the analytical results, we apply the abstract findings to concrete equations of the Moore-Gibson-Thompson type. Additionally, we employ numerical computations to further elucidate the analytical results.