Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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BLOW-UP PHENOMENA FOR A QUASILINEAR PARABOLIC EQUATION WITH TIME-DEPENDENT COEFFICIENTS UNDER NONLINEAR BOUNDARY FLUX

  • Kwon, Tae In (Department of Mathematics Changwon National University) ;
  • Fang, Zhong Bo (School of Mathematical Sciences Ocean University of China)
  • Received : 2018.03.06
  • Accepted : 2018.07.12
  • Published : 2018.08.15
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Abstract

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.

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References

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