Gradient estimates for porous medium equations under the Ricci flow

A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained.

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Veröffentlicht in:	Applied Mathematics-A Journal of Chinese Universities 2016-12, Vol.31 (4), p.481-490
Hauptverfasser:	Shen, Li-ju, Yao, Sha, Zhang, Guang-ying, Ren, Xin-an
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Mathematical analysis Mathematics Mathematics and Statistics Porous media Riemann manifold Theorems 多孔介质方程整体解梯度估计正解渗流非紧黎曼流形
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Beschreibung
Zusammenfassung:	A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained.
ISSN:	1005-1031 1993-0445
DOI:	10.1007/s11766-016-3368-1