Eigenvalue Asymptotics in Isothermal Forced Elongation

In this paper, we consider the formal linearization of the governing equations of forced elongation in the isothermal regime. We give an asymptotic characterization of the spectrum of the associated strongly continuous semigroup. To this end, we develop rigorous asymptotic techniques to determine the asymptotic behavior of the eigenvalues by solving a characteristic integral equation in a generalized sector of the complex plane. The spectral mapping theorem, relating the spectrum of the semigroup to the spectrum of its generator, proves essential. Numerical evidence will be given to demonstrate the accuracy of our asymptotic predictions