Gazzola, Filippo; Grunau, Hans-Christoph Eventual local positivity for a biharmonic heat equation in \(\mathbb R^n\). (English) Zbl 1153.35304 Discrete Contin. Dyn. Syst., Ser. S 1, No. 1, 83-87 (2008). Summary: We study the positivity preserving property for the Cauchy problem for the linear fourth-order heat equation. Although the complete positivity preserving property fails, we show that it holds eventually on compact sets. Cited in 25 Documents MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B50 Maximum principles in context of PDEs 35K30 Initial value problems for higher-order parabolic equations Keywords:positivity preserving; linear fourth-order heat equation PDFBibTeX XMLCite \textit{F. Gazzola} and \textit{H.-C. Grunau}, Discrete Contin. Dyn. Syst., Ser. S 1, No. 1, 83--87 (2008; Zbl 1153.35304) Full Text: DOI