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dc.contributor.authorFalconer, Kenneth John
dc.contributor.authorHu, Jiaxin
dc.contributor.authorSun, Yuhua
dc.identifier.citationFalconer , 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 .
dc.identifier.otherPURE: 5485274
dc.identifier.otherPURE UUID: 1165f3b4-9bb4-48e2-9497-8021a3da9512
dc.identifier.otherScopus: 84870042560
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055269
dc.description.abstractWe 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.
dc.relation.ispartofProceedings of the Royal Society of Edinburgh, Section A: Mathematicsen
dc.rights(c) 2012 The Royal Society of Edinburghen
dc.subjectQA Mathematicsen
dc.titleInhomogeneous parabolic equations on unbounded metric measure spacesen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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