Inhomogeneous parabolic equations on unbounded metric measure spaces (2011)
by
Kenneth J. Falconer
,
Jiaxin Hu
,
Yuhua Sun
BibTeX
@MISC{Falconer11inhomogeneousparabolic,
author = {Kenneth J. Falconer and Jiaxin Hu and Yuhua Sun},
title = {Inhomogeneous parabolic equations on unbounded metric measure spaces},
year = {2011}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
We study the inhomogeneous semilinear parabolic equation ut =∆u+ u p + f(x), with source term f independent of time and subject to f(x) � 0 and with u(0,x)=ϕ(x) � 0, for the very general setting of a metric measure space. 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, depending on the value of p relative to a critical exponent. 1.
