Electronic Research Archive

August 2019 , Volume 27

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A conjecture on cluster automorphisms of cluster algebras
Peigen Cao, Fang Li, Siyang Liu and Jie Pan
2019, 27: 1-6 doi: 10.3934/era.2019006 +[Abstract](120) +[HTML](69) +[PDF](313.12KB)

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.

On the time decay in phase–lag thermoelasticity with two temperatures
Antonio Magaña, Alain Miranville and Ramón Quintanilla
2019, 27: 7-19 doi: 10.3934/era.2019007 +[Abstract](63) +[HTML](27) +[PDF](365.0KB)

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.

2018  Impact Factor: 0.263



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