加权源伪抛物方程的爆破时间和爆破率

Pub Date : 2020-01-01 DOI:10.4134/CKMS.C200035

Huafei Di, Y. Shang

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引用次数: 0

摘要

本文研究了在任意光滑有界区域Ω∧Rn (n≥1)上，具有加权源ut−4u−4ut = a(x)f(u)的伪抛物型方程在Dirichlet(或Neumann)边界条件下的爆破现象。首先得到了这类问题解的爆破时间的上界和下界。此外，我们还给出了在一些合适条件下解的爆破率的估计。最后，提出了三个模型来说明我们的主要结果。在某些特殊情况下，我们甚至可以得到爆破时间和爆破速率的精确值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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BLOW-UP TIME AND BLOW-UP RATE FOR PSEUDO-PARABOLIC EQUATIONS WITH WEIGHTED SOURCE

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source ut−4u− 4ut = 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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