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Zeitschrift für Analysis und ihre Anwendungen


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Volume 29, Issue 4, 2010, pp. 437–449
DOI: 10.4171/ZAA/1417

Published online: 2010-10-02

A Necessary Condition for the Instantaneous Shrinking Property of Solutions to a Semilinear Heat Equation

Qiyu Sun[1]

(1) Zhejiang University, China

In the paper, we prove that if the support of the solution of a semilinear heat equation has the instantaneous shrinking property, then the initial data must vanish at infinity. We apply the weak comparison principle to prove this conclusion. We also give an example to illustrate our results.

Keywords: Comparison principles, instantaneous shrinking of the support, strong absorption, semilinear heat equation

Sun Qiyu: A Necessary Condition for the Instantaneous Shrinking Property of Solutions to a Semilinear Heat Equation. Z. Anal. Anwend. 29 (2010), 437-449. doi: 10.4171/ZAA/1417