Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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BLOW-UP AND GLOBAL SOLUTIONS FOR SOME PARABOLIC SYSTEMS UNDER NONLINEAR BOUNDARY CONDITIONS

  • Guo, Limin (School of Mathematical Sciences Qufu Normal University) ;
  • Liu, Lishan (School of Mathematical Sciences Qufu Normal University) ;
  • Wu, Yonghong (Department of Mathematics and Statistics Curtin University) ;
  • Zou, Yumei (Department of Statistics and Finance Shandong University of Science and Technology)
  • Received : 2018.08.07
  • Accepted : 2019.03.04
  • Published : 2019.07.01
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Abstract

In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $({\varrho}(u))_t$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

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References

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