• Login
  • Register
  • Search

Asymptotic behaviors of heat equation associated with symmetric a-stable-like process

Yue Hu, Mingjie Liang

Abstract


This paper is devoted to asymptotic behaviors of heat equation corresponding to symmetric a-stable-like process X:=(Xt)t≥0 on metric measure space.Denote pt(x,y) the heat kernel of the process, and by u(t,x) the solution of the associated heat equation.We then establish asymptotic behaviors between pt(x,y) and u(t,x) ,which enjoy similar properties of these in Riemannian manifolds.

Keywords


a-stable-like process; Heat kernel; Heat equation; Asymptotic behaviors

Full Text:

PDF

Included Database


References


[1] Vázquez J L.Asymptotic behaviour methods for the heat equation.Convergence to the Gaussian[J].arXiv:1706.10034.

[2] Vázquez J L.Asymptotic behaviour for the heat equation in hyperbolic space[J].arXiv:1811.09034.

[3] Anker J P,Papageorgiou E,Zhang H W.Asymptotic behavior of solutions to the heat equation on noncompact symmetric spaces[J].arXiv:2112.01323.

[4] Grigor’yan A,Papageorgiou E,Zhang H W.Asymptotic behavior of the heat semigroup on certain Riemannian manifolds[J].arXiv:2205.06105.

[5] Grigor’yan A,Hu J.Upper bounds of heat kernels on doubling spaces[J].Moscow Math.J,2014,14:505--563.

[6] Chen Z Q,Kumagai T,Wang J.Stability of heat kernel estimates for symmetric non-local Dirichlet forms[J].Memoirs Amer.Math.Soc.,2021,271:1330.

[7] Chen Z Q,Kumagai T,Wang J.Stability of parabolic Harnack inequalitiess for symmetric non-local Dirichlet forms[J].J.Eur.Math.Soc.,2020,22:3747--3803.




DOI: http://dx.doi.org/10.18686/ahe.v7i26.10356

Refbacks
Copyright © 2020 Universe Scientific Publishing. All rights reserved.