Equiconvergence with Fourier Series for Non-Classical Sturm-Liouville Problems

Abstract

Sturm-Liouville type boundary-value problems arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of chemistry, aerodynamics, electrodynamics of complex medium or polymer rheology. For example the vibration of a homogeneous loaded strings, the earth's free oscillations, the interaction of atomic particles, sound, surface waves, heat transfer in a rod with heat capacity concentrated at the ends, electromagnetic waves and gravitational waves can be solved using the Sturmian theory. A large class of physical problems require the investigation of the Sturm-Liouville type problems with discontinuities. Examples are vibration problems under various loads such as a vibrating string with a tip mass or heat conduction through a liquid solid interface.