Note on blow-up of solutions for a porous medium equation with convection and boundary flux

Volume 128 / 2012

Zhiyong Wang, Jingxue Yin Colloquium Mathematicum 128 (2012), 223-228 MSC: Primary 35K55; Secondary 35B33. DOI: 10.4064/cm128-2-7

Abstract

De Pablo et al. [Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 513–530] considered a nonlinear boundary value problem for a porous medium equation with a convection term, and they classified exponents of nonlinearities which lead either to the global-in-time existence of solutions or to a blow-up of solutions. In their analysis they left open the case of a certain critical range of exponents. The purpose of this note is to fill this gap.

Authors

  • Zhiyong WangDepartment of Mathematics
    Jilin University
    Changchun, 130012, P.R. China
    e-mail
  • Jingxue YinSchool of Mathematical Sciences
    South China Normal University
    Guangzhou, 510631, P.R. China
    e-mail

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