Inhomogeneous parabolic equations on unbounded metric measure spaces

Kenneth John Falconer, Jiaxin Hu, Yuhua Sun

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
3 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)1003-1025
JournalProceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume142
Issue number5
Early online date20 Sept 2012
DOIs
Publication statusPublished - Oct 2012

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