Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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BLOW-UP TIME AND BLOW-UP RATE FOR PSEUDO-PARABOLIC EQUATIONS WITH WEIGHTED SOURCE

  • Di, Huafei (School of Mathematics and Information Science Guangzhou University) ;
  • Shang, Yadong (School of Mathematics and Information Science Guangzhou University)
  • Received : 2020.02.05
  • Accepted : 2020.07.30
  • Published : 2020.10.31
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Abstract

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source ut - △u - △ut = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ ℝn (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.

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References

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