带延迟的非线性双曲系统的爆炸研究

Q1 Mathematics

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-23 DOI:10.1016/j.padiff.2024.100984

Mohammad Kafini, Mohammad M. Al-Gharabli, Adel M. Al-Mahdi

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引用次数: 0

摘要

这项工作研究的是以摩擦阻尼和非线性源为特征的波方程系统。这两个方程受到恒定延迟的影响。通过证明存在在有限时间内炸毁的负初始能量解，我们证明了炸毁结果。莱文的凹性方法是证明的基础。此外，通过对下限的估计，我们从下往上控制了炸毁时间。

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 study of a nonlinear hyperbolic system with delay

This work examines a system of wave equations that feature frictional damping and nonlinear sources. The two equations are affected by constant delay. By demonstrating that there exist solutions with negative initial energy that blow up in a finite amount of time, we prove a blow-up result. Levine’s concavity approach is a basis of the proof. Additionally, by estimating the lower bound, we dominate the blow-up time from below.

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