加权源伪抛物方程的爆破时间和爆破率

IF 0.5 Q3 MATHEMATICS

Communications of the Korean Mathematical Society 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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来源期刊

Communications of the Korean Mathematical Society MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： This journal endeavors to publish significant research and survey of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of four issues (January, April, July, October).