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arXiv · 1103.5533

Inhomogeneous parabolic equations on unbounded metric measure spaces

Kenneth J. Falconer·Jiaxin Hu·Yuhua Sun
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Abstract

We study inhomogeneous semilinear parabolic equations with source term f independent of time u_{t}=Δu+u^{p}+f(x) on a metric measure space, subject to the conditions that f(x)\geq 0 and u(0,x)=ϕ(x)\geq 0. 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. This paper generalizes previous results on Euclidean spaces to general metric measure spaces.

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Kenneth J. Falconer, Jiaxin Hu, Yuhua Sun. 2011-03-29. Inhomogeneous parabolic equations on unbounded metric measure spaces. https://arxiv.org/abs/1103.5533

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