Muñoz Rivera, Jaime E.; Naso, Maria Grazia On the decay of the energy for systems with memory and indefinite dissipation. (English) Zbl 1115.35024 Asymptotic Anal. 49, No. 3-4, 189-204 (2006). Summary: We study the asymptotic behavior of the viscoelastic system with nondissipative kernels. We show that the uniform decay of the energy depends on the decay of the kernel, the positivity of the kernel in \(t=0\) and some smallness condition. That is, if the kernel \(g\in C^2(\mathbb{R}^+)\) with \(g(0)>0\), decays exponentially to zero then the solution decays exponentially to zero. On the other hand, if the kernel decays polynomially as \(t^{-p}\) then the corresponding solutions also decays polynomially to zero with the same rate decay. Cited in 49 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35L90 Abstract hyperbolic equations 74D05 Linear constitutive equations for materials with memory Keywords:materials with memory; asymptotic stability PDFBibTeX XMLCite \textit{J. E. Muñoz Rivera} and \textit{M. G. Naso}, Asymptotic Anal. 49, No. 3--4, 189--204 (2006; Zbl 1115.35024)