Studies on the linear equations of melt-spinning of viscous fluids

We discuss the linearized equations of fiber spinning in the non-isothermal viscous regime. We prove that the solutions of the hyper-bolic equations of fiber spinning are generated by an eventually com-pact semigroup of bounded linear operators. This result gives us the justification to relate the stability of the semigroup to the numerical resolution of the spectrum of its generator. We report several numer-ical findings, confirming prior results on the stability of solutions for the equations of melt-spinning. Key words and phrases: Melt-spinning; spectrum; linear stabilit