Abstract
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. Ṫ+τqT̈+τq22T⃛=κ△T+κτT△Ṫ+κτT22△T̈on 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). τTτq>2−3; (ii). 2−3≥τTτq>(1+κτTλ1)2+(κτTλ1)2+(κτTλ1)3−(1+κτTλ1)κτTλ1(1+κτTλ1), where λ1 is the smallest eigenvalue of the negative Laplacian on Ω with Dirichlet boundary condition.
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