Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2010-10-02
A Necessary Condition for the Instantaneous Shrinking Property of Solutions to a Semilinear Heat EquationQiyu Sun (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