Li-Yau estimates for a nonlinear parabolic equation on manifolds. (English) Zbl 1309.53055
Summary: In this paper, we derive Li-Yau gradient estimates for the positive solution of a nonlinear parabolic equation \(u_t=\Delta u -qu-au(\ln u)^\alpha\), where \(q\) is a \(C^2\) function and \(a,\alpha\) are constants, on a complete manifold (\(M\),\(g\)) with Ricci curvature bounded below. The results generalize classical Li-Yau gradient estimates and some recent works on this direction.
MSC:
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
References:
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