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.
Cite this article
Qiyu Sun, A Necessary Condition for the Instantaneous Shrinking Property of Solutions to a Semilinear Heat Equation. Z. Anal. Anwend. 29 (2010), no. 4, pp. 437–449DOI 10.4171/ZAA/1417