Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory

Pub Date : 2020-06-01 DOI:10.4208/jpde.v33.n3.5
Jiahui Huang
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Abstract

In this paper, we investigate a reaction-diffusion equation ut−duxx = au+ ∫ t 0 u p(x,τ)dτ+k(x) with double free boundaries. We study blowup phenomena in finite time and asymptotic behavior of time-global solutions. Our results show if ∫ h0 −h0 k(x)ψ1dx is large enough, then the blowup occurs. Meanwhile we also prove when T∗<+∞, the solution must blow up in finite time. On the other hand, we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently. AMS Subject Classifications: 35K20, 35R35, 92B05 Chinese Library Classifications: O175
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一类具有非线性记忆的自由边界问题的爆破与渐近性质
本文研究了一类具有双自由边界的反应扩散方程ut - duxx = au+∫t 0 u p(x,τ)dτ+k(x)。研究了有限时间内的爆破现象和时间全局解的渐近性质。我们的结果表明,如果∫h0−h0 k(x)ψ1dx足够大,则会发生爆炸。同时也证明了当T * <+∞时,解在有限时间内必须爆破。另一方面,我们证明了在初始基准足够小的情况下,解以指数速率衰减,两个自由边界收敛于有限极限。AMS学科分类:35K20, 35R35, 92B05中文图书馆分类:O175
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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