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- W4380558997 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." @default.
- W4380558997 created "2023-06-14" @default.
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- W4380558997 date "2023-06-12" @default.
- W4380558997 modified "2023-10-16" @default.
- W4380558997 title "Supercaloric functions for the porous medium equation in the fast diffusion case" @default.
- W4380558997 doi "https://doi.org/10.48550/arxiv.2306.07155" @default.
- W4380558997 hasPublicationYear "2023" @default.
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