English

Heat equation and Poisson equation in matrix geometry

Quantum Algebra 2013-11-26 v1 Differential Geometry Operator Algebras

Abstract

In this paper, we study the Poisson equation and heat equation in a model matrix geometry MnM_n. Our main results are about the Poisson equation and global behavior of the heat equation on MnM_n. We can show that if c0c_0 is the initial positive definite matrix in MnM_n, then c(t)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.

Keywords

Cite

@article{arxiv.1311.6341,
  title  = {Heat equation and Poisson equation in matrix geometry},
  author = {Jiaojiao Li},
  journal= {arXiv preprint arXiv:1311.6341},
  year   = {2013}
}
R2 v1 2026-06-22T02:14:22.688Z