Energy decay rate of Mixed Dual-Phase-Lag Heat Conduction System

Abstract

This paper studies the dual-phase-lag heat conduction system, the model of which improves the classical Fourier equation by adding two positive delay variables. Assume that these two delay parameters are vanished in a subregion of the spatial domain [-1,1], which yields a mixed heat conduction system. By the resolvent estimate, we obtain two different energy decay rate of the system under certain conditions respect to the relationship between these two delay parameters. Especially, a faster energy decay rate is proved compared to the one with the globally positive delay parameters conditions are fulfilled.