[L'équation de la chaleur pour une géométrie matricielle modèle]
Dans cet article, nous étudions l'équation de la chaleur pour la géométrie matricielle modèle . Nos principaux résultats concernent le comportement global de l'équation de la chaleur. Nous parvenons à montrer que, si la matrice initiale est définie positive dans , alors 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 . Our main results are about the global behavior of the heat equation on . We can show that if is the initial positive definite matrix in , then 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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@article{CRMATH_2015__353_4_351_0,
author = {Jiaojiao Li},
title = {Heat equation in a model matrix geometry},
journal = {Comptes Rendus. Math\'ematique},
pages = {351--355},
publisher = {Elsevier},
volume = {353},
number = {4},
year = {2015},
doi = {10.1016/j.crma.2014.10.024},
language = {en},
}
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/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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