Heat equation and Poisson equation in matrix geometry

Abstract

In this paper, we study the Poisson equation and heat equation in a model matrix geometry $M_n$. Our main results are about the Poisson equation and global behavior of the heat equation on $M_n$. We can show that if $c_0$ is the initial positive definite matrix in $M_n$, 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.

References in corpus (3)

• Levi-Civita's Theorem for Noncommutative Tori
• Noncommutative Ricci flow in a matrix geometry
• Deformed Noncommutative Tori

Cited by in corpus (1)

• L2 norm preserving flow in matrix geometry