Finite propagation speed for solutions of the parabolic {$p$}-Laplace equation on manifolds

We consider a class of degenerate parabolic equations containing the parabolic $p$-Laplace equation, on Riemannian manifolds. We prove that, on arbitrary manifolds, bounded solutions of such equations have finite propagation speed, and show that the rate of propagation can be estimated in terms of bounds on the Ricci curvature. The main technical tool in the proof is a new mean value type inequality for bounded solutions.

2010 Mathematics Subject Classification

Primary 58Jxx. Secondary 35B45, 35K55, 35K65.

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Published 1 January 2005