In this paper, we investigate new classes of viscoelastic Timoshenko-Ehrenfest systems under the presence of full or partial memory effects. Our achievements rely on recent approaches to the theory of dissipative structure for systems of differential equations, by featuring optimal pointwise estimates in the Fourier space, L ²-estimates for the solutions, and explicit energy decay rates depending on the viscoelastic damping coupling. Therefore, under a complete stability analysis, original results as well as improvements of previous work in the literature are our main findings.

A mass of meson, an interacting particle of mass intermediate between proton and neutron, is described by an eigenvalue problem of a certain second order ordinary differential equation. In this paper we consider this eigenvalue problem from the viewpoint of the exact WKB analysis. We find that a connection problem in the complex plane corresponds to this eigenvalue problem. Through studying this connection problem by using the exact WKB method, we give an explicit form of a secular equation for the eigenvalue problem modulo exponentially small terms. Comparisons with numerical calculations are also discussed.