Aronson-Benilan estimates for the fast diffusion equation under the Ricci flow

作者：Cao, Huai-Dong; Zhu, Meng^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2018, 170: 258-281.

DOI：10.1016/j.na.2018.01.006

• POROUS-MEDIUM EQUATION
• NONLINEAR HEAT-EQUATIONS

We study the fast diffusion equation with a linear forcing term, @@@ partial derivative u/partial derivative t = div(|u|p(-1)del u) + Ru, (0.1) @@@ under the Ricci flow on a complete manifold M such that M x R-2 has bounded curvature and nonnegative isotropic curvature, where 0 < p < 1 and R = R(x, t) is the evolving scalar curvature of M at time t. We prove Aronson-Benilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions of (0.1). In addition, we use similar method to prove certain Li-Yau-Hamilton estimates for the heat equation and conjugate heat equation which extend those obtained in Cao and Hamilton (2009), Cao (2008), and Kuang and Zhang (2008) to the noncompact setting.

• 出版日期2018-5
• 单位华东师范大学