A Liouville-type theorem of a weighted semilinear parabolic equation on weighted manifolds with boundary

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Abstract

We derive a Liouville-type theorem for positive ancient solutions to a weighted semilinear parabolic equation with a Dirichlet boundary condition on complete noncompact weighted manifolds with a compact boundary. This result can be viewed as an extension of Dung et al.’s work on a linear heat equation.

Keywords

Liouville-type theorem / ancient solution / semilinear parabolic equation / weighted manifold / gradient estimate

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