# American Institute of Mathematical Sciences

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2688-1594

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## Electronic Research Archive

August 2019 , Volume 27

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2019, 27: 1-6 doi: 10.3934/era.2019006 +[Abstract](120) +[HTML](69) +[PDF](313.12KB)
Abstract:

A cluster automorphism is a \begin{document}$\mathbb{Z}$\end{document}-algebra automorphism of a cluster algebra \begin{document}$\mathcal A$\end{document} satisfying that it sends a cluster to another and commutes with mutations. Chang and Schiffler conjectured that a cluster automorphism of \begin{document}$\mathcal A$\end{document} is just a \begin{document}$\mathbb{Z}$\end{document}-algebra homomorphism of a cluster algebra sending a cluster to another. The aim of this article is to prove this conjecture.

2019, 27: 7-19 doi: 10.3934/era.2019007 +[Abstract](63) +[HTML](27) +[PDF](365.0KB)
Abstract:

The aim of this paper is to study the time decay of the solutions for two models of the one-dimensional phase-lag thermoelasticity with two temperatures. The first one is obtained when the heat flux vector and the inductive temperature are approximated by a second-order and first-order Taylor polynomial, respectively. In this case, the solutions decay in a slow way. The second model that we consider is obtained taking first-order Taylor approximations for the inductive thermal displacement, the inductive temperature and the heat flux. The decay is, therefore, of exponential type.

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