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Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions
Open Mathematics ( IF 1.7 ) Pub Date : 2020-01-01 , DOI: 10.1515/math-2020-0088
Huimin Tian 1 , Lingling Zhang 1, 2
Affiliation  

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

中文翻译:

Neumann 边界条件下具有瞬态系数的非局域反应扩散方程的爆破分析

摘要 本文研究了具有瞬态系数的非局域反应扩散方程在Neumann边界条件下的膨胀分析。通过构造一些合适的辅助函数并使用微分不等式技术,我们展示了一些充分条件,以确保解 u ( x , t ) u(x, t) 在适当的测度意义上在有限时间内爆炸。此外,在一些适当的假设下推导出爆破时间的上限和下限。最后,给出了两个例子来说明我们主要结果的应用。
更新日期:2020-01-01
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