Heat equation in a model matrix geometry

Li, Jiaojiao

Comptes Rendus. Mathématique, Tome 353 (2015) no. 4, pp. 351-355.

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.

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.

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