Let (M,g) be an n dimensional complete Riemannian manifold. In this article we prove local Li-Yau type gradient estimates for all positive solutions to the nonlinear parabolic equation
along the generalised geometric flow on M. Here is a smooth potential function and a is an arbitrary constant. As an application we derive a global estimate and a space-time Harnack inequality.
Submitted December 8, 2014. Published January 8, 2015.
Math Subject Classifications: 35K55, 53C21, 53C44, 58J35.
Key Words: Gradient estimates; Harnack inequalities; parabolic equations; geometric flows.
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| Abimbola Abolarinwa |
Department of Mathematics, University of Sussex
Brighton, BN1 9QH, United Kingdom
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