Inhomogeneous parabolic equations on unbounded metric measure spaces
Published online by Cambridge University Press: 20 September 2012
Abstract
We study the inhomogeneous semilinear parabolic equation
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.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 5 , October 2012 , pp. 1003 - 1025
- Copyright
- Copyright © Royal Society of Edinburgh 2012
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