'Wave type' spectrum of the Gurtin-Pipkin equation of the second order

Abstract

We study the complex part of the spectrum of the the Gurtin-Pipkin integral-differential equation of the second order in time. We consider the model case when the kernel is a sum of exponentials $a_k\exp (-b_k)$ with $a_k=1/k^\a$, $b_k=k^\b$. We show that there are two complex sequences of points of the spectrum asymptotically close to the spectrum points of the wave equation.

Two typos are corrected

Cited by in corpus (2)

• Spectra of the Gurtin-Pipkin type equations with the kernel, depending on the parameter
• Correct solvability of hyperbolic Volterra equations with kernels depending on the parameter