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Global existence and blowup for a degenerate parabolic equation with a free boundary

Volume 124 / 2020

Youpeng Chen, Xingying Liu Annales Polonici Mathematici 124 (2020), 1-31 MSC: Primary 35B35, 35B40, 35K51; Secondary 35K65, 35R35. DOI: 10.4064/ap171230-26-5 Published online: 13 December 2019

Abstract

This paper deals with a free boundary problem for a degenerate parabolic equation. For such a problem, we mainly study the blowup property and global existence of solutions. Our results show that blowup occurs if the initial datum is sufficiently large, while the solution is global and fast if the initial data is sufficiently small, and that the existence of a global slow solution is possible when the initial data is suitably large.

Authors

  • Youpeng ChenSchool of Mathematics and Information Science
    Nanjing Normal Institute of Special Education
    Nanjing 210038, P.R. China
    e-mail
  • Xingying LiuSchool of Mathematics and Statistics
    Yancheng Normal University
    Yancheng 224002, P.R. China

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