×

Eventual local positivity for a biharmonic heat equation in \(\mathbb R^n\). (English) Zbl 1153.35304

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.

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
PDFBibTeX XMLCite
Full Text: DOI