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Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison

Published online by Cambridge University Press:  14 November 2011

Nicholas D. Alikakos  and
Rouben Rostamian
Nicholas D. Alikakos
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996, U.S.A.
Rouben Rostamian
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, U.S.A.
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Synopsis

We consider the Cauchy problem for the porous medium equation in one space dimension, with initial data which are locally integrable. We measure the asymptotic behaviour of the initial data near infinity in an integral sense and relate this to the pointwise rate of growth or decay of solution for large time. The emphasis is on a novel comparison method wherein the initial data are rearranged on the ×-axis to form a sequence of Dirac δ-masses. By using the explicit solution in the latter case, we derive upper and lower bounds for the solution to the original problem by comparisons.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 1 - 10
Copyright
Copyright © Royal Society of Edinburgh 1985

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