期刊
ACTA MATHEMATICA SINICA-ENGLISH SERIES
卷 27, 期 6, 页码 1071-1078出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10114-011-8474-7
关键词
Nonlinear parabolic equations; Li-Yau inequalities; Harnack differential inequalities; gradient estimates
资金
- China Scholarship Council of China [2007U13020]
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive solution to a simple nonlinear parabolic equation partial derivative tu - Delta u + au log u + qu on M x (0,a), where a is a constant and q is a C (2) function. This result can be compared with the ones of Ma (JFA, 241, 374-382 (2006)) and Yang (PAMS, 136, 4095-4102 (2008)). Also, we obtain Hamilton's gradient estimate for the Schodinger equation. This can be compared with the result of Ruan (JGP, 58, 962-966 (2008)).
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