Year: 2024
Type: article
Abstract: We study a generalized class of supersolutions, so-called supercaloric functions, to the porous medium equation in the fast diffusion case. Supercaloric functions are defined as lower semicontinuous functions obeying a parabolic comparison principle. We prove that bounded supercaloric functions are weak supersolutions. In the supercritical range, we show that unbounded supercaloric functions can be divided into two mutually exclusive classes dictated by the Barenblatt solution and the infinite point-source solution, and give several characterizations for these classes. Furthermore, we study the pointwise behavior of supercaloric functions and obtain connections between supercaloric functions and weak supersolutions.
DOI: 10.4171/rmi/1507
Authors: Kristian Moring, Christoph Scheven
Institutions: University of Salzburg, University of Duisburg-Essen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404828987