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Supercaloric functions for the porous medium equation

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Abstract

In the slow diffusion case, unbounded supersolutions of the porous medium equation are of two totally different types, depending on whether the pressure is locally integrable or not. This criterion and its consequences are discussed.

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Authors and Affiliations

  1. Department of Mathematics, Aalto University, P.O. Box 11100, 00076, Helsinki, Finland

    Juha Kinnunen & Pekka Lehtelä

  2. Department of Mathematics, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Peter Lindqvist

  3. Department of Mathematics and Statistics, University of Jyvaskylä, P.O. Box 35, 40014, Jyväskylä, Finland

    Mikko Parviainen

Authors
  1. Juha Kinnunen
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  2. Pekka Lehtelä
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  3. Peter Lindqvist
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  4. Mikko Parviainen
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Corresponding author

Correspondence to Juha Kinnunen.

Additional information

The research is supported by the Academy of Finland, the Emil Aaltonen Foundation and the Norwegian Research Council.

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Kinnunen, J., Lehtelä, P., Lindqvist, P. et al. Supercaloric functions for the porous medium equation. J. Evol. Equ. 19, 249–270 (2019). https://doi.org/10.1007/s00028-018-0474-y

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  • DOI: https://doi.org/10.1007/s00028-018-0474-y

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