J Austral Math Soc Ser A 48 pp246--263, 1990.

The Persistence of Logconacivity for Positive Solutions of the One Dimensional Heat Equation

G. Keady

Abstract

Consider positive solutions of the one dimensional heat equation. The space variable x lies in (-a, a): the time variable t in (0, ¥). When the solution u satisfies (i) u(±a, t) = 0, and (ii) u(·, 0) is logoncave, we give a new proof based on the Maximum Principle, that, for any fixed t > 0, u(·, t) remains logoncave. The same proof techniques are used to establish several new results related to this, including results concerning joint concavity in (x, t) similar to those considered in Kennington [15].

1980 AMS Subject Classification (1985 Revision): 35K05

Browse the article

Authors

G. Keady

Department of Mathematics, University of Western Australia, Nedlands, W. A. 6009, Australia.