TY  - JOUR
AU  - Liu, Hao-Yue
AU  - Zhang, Wei
PY  - 2024
TI  - Neumann gradient estimate for nonlinear heat equation under integral Ricci curvature bounds
JO  - AIMS Mathematics
SP  - 3881
EP  - 3894
VL  - 9
IS  - 2
AB  - In this paper, we consider a Li-Yau gradient estimate on the positive solution to the following nonlinear parabolic equation         ∂          ∂      t        f  =  Δ  f  +  a  f  (  ln  ⁡  f      )          p      with Neumann boundary conditions on a compact Riemannian manifold satisfying the integral Ricci curvature assumption, where    p  ≥  0 is a real constant. This contrasts Olivé's gradient estimate, which works mainly for the heat equation rather than nonlinear parabolic equations and the result can be regarded as a generalization of the Li-Yau [P. Li, S. T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math.,  156 (1986), 153–201] and Olivé [X. R. Olivé, Neumann Li-Yau gradient estimate under integral Ricci curvature bounds, Proc. Amer. Math. Soc.,  147 (2019), 411–426] gradient estimates.
UR  - https://doi.org/10.3934/math.2024191
DO  - 10.3934/math.2024191