[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2014.008

EVOLUTION EQUATIONS ON A RIEMANNIAN MANIFOLD WITH A LOWER RICCI CURVATURE BOUND

Chang, Jeongwook (Department of Mathematics Education, Dankook University)

Publication Information

East Asian mathematical journal / v.30, no.1, 2014 , pp. 79-91 More about this Journal

Abstract

We consider the parabolic evolution differential equation such as heat equation and porus-medium equation on a Riemannian manifold M whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by 0 on some amount of M. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.

Keywords

heat equation; porus medium equation; Harnack inequality; Ricci curvature;

Citations & Related Records

Reference

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