Inhomogeneous parabolic equations on unbounded metric measure spaces
View/ Open
Date
10/2012Keywords
Metadata
Show full item recordAltmetrics Handle Statistics
Altmetrics DOI Statistics
Abstract
We study the inhomogeneous semilinear parabolic equation ut = Δu + up + 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.
Citation
Falconer , K J , Hu , J & Sun , Y 2012 , ' Inhomogeneous parabolic equations on unbounded metric measure spaces ' , Proceedings of the Royal Society of Edinburgh, Section A: Mathematics , vol. 142 , no. 5 , pp. 1003-1025 . https://doi.org/10.1017/S0308210511000539
Publication
Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Status
Peer reviewed
ISSN
0308-2105Type
Journal article
Rights
(c) 2012 The Royal Society of Edinburgh
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.