On the regularity and stability of the dual-phase-lag equation

In this paper we consider the following linear partial differential equation which is usually seen as an approximation to the dual-phase-lag heat equation proposed by Tzou. [Formula presented] on a bounded domain Ω in Rⁿ with smooth boundary. We obtain analyticity for the associated C₀−semigroup. Moreover, we also obtain exponential stability of the solutions by spectrum analysis and Hurwitz criterion under one of the following conditions: (i). [Formula presented] (ii). [Formula presented] where λ₁ is the smallest eigenvalue of the negative Laplacian on Ω with Dirichlet boundary condition.