Comptes Rendus
Differential geometry
Heat equation in a model matrix geometry
Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 351-355.

In this paper, we study the heat equation in a model matrix geometry Mn. Our main results are about the global behavior of the heat equation on Mn. We can show that if c0 is the initial positive definite matrix in Mn, then c(t) exists for all time and is positive definite too. We can also show the entropy stability of the solutions to the heat equation.

Dans cet article, nous étudions l'équation de la chaleur pour la géométrie matricielle modèle Mn. Nos principaux résultats concernent le comportement global de l'équation de la chaleur. Nous parvenons à montrer que, si la matrice initiale c0 est définie positive dans Mn, alors c(t) existe pour tout temps et reste définie positive. Nous montrons également la stabilité de l'entropie des solutions de l'équation de la chaleur.

Published online:
DOI: 10.1016/j.crma.2014.10.024

Jiaojiao Li 1

1 Department of Mathematics, Henan Normal University, Xinxiang, 453007, China
     author = {Jiaojiao Li},
     title = {Heat equation in a model matrix geometry},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {351--355},
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     year = {2015},
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     language = {en},
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Jiaojiao Li. Heat equation in a model matrix geometry. Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 351-355. doi : 10.1016/j.crma.2014.10.024.

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The research is partially supported by the National Natural Science Foundation of China (No. 11301158, No. 11271111).

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