Inhomogeneous parabolic equations on unbounded metric measure spaces
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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.
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 . DOI: 10.1017/S0308210511000539
Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
(c) 2012 The Royal Society of Edinburgh
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