Author

Jia-Min Yang

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Preprint Sep 2026

Hamilton's gradient estimates and Liouville theorems for $u_{t}=\Delta u^{m}+au\log u+bu$ on Riemannian manifolds

In this paper, we apply Nash-Moser iteration and Saloff-Coste's Sobolev inequalities to derive gradient estimates for positive solutions to a class of nonlinear parabolic equations of the form \begin{equation*} u_{t}=\Delta u^{m}+a(x, t)u\log u+b(x, t)u, \quad 1-\frac{2}{n}<m<1 \quad \text{or}\quad 1<m<1+\frac{1}{1+\sq...

Jun-Ping-Wang-Tong Sun, Jia-Min Yang · 0 citations

Preprint Sep 2026

Hamilton-Type Gradient Estimates for Porous Medium and Fast Diffusion Equations on Riemannian Manifolds for all exponents

We establish local Hamilton-type gradient estimates for positive $C^{2,1}$ solutions of $u_t=\Delta u^m$ on complete Riemannian manifolds whose Ricci curvature is bounded from below. For every fixed $m>1$ and every fixed $0<m<1$, there exist $\beta=\beta(m,n)>0$ and $C=C(m,n)>0$ such that a solution $0<u\leqslant A$ in...

Jun-Ping-Wang-Tong Sun, Jia-Min Yang · 0 citations