Inhomogeneous parabolic equations on unbounded metric measure spaces
Mathematical Physics
2011-03-30 v1 math.MP
Abstract
We study inhomogeneous semilinear parabolic equations with source term f independent of time u_{t}={\Delta}u+u^{p}+f(x) on a metric measure space, subject to the conditions that f(x)\geq 0 and u(0,x)=\phi(x)\geq 0. By establishing Harnack-type inequalities in time t and some powerful estimates, we give sufficient conditions for non-existence, local existence, and global existence of weak solutions. This paper generalizes previous results on Euclidean spaces to general metric measure spaces.
Keywords
Cite
@article{arxiv.1103.5533,
title = {Inhomogeneous parabolic equations on unbounded metric measure spaces},
author = {Kenneth J. Falconer and Jiaxin Hu and Yuhua Sun},
journal= {arXiv preprint arXiv:1103.5533},
year = {2011}
}