高阶强耗散Kirchhoff型非线性波动方程解的局部存在性和爆破

Guoguang Lin, Yunlong Gao, Yuting Sun
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引用次数: 10

摘要

本文研究了具有强耗散的高阶Kirchhoff型非线性波动方程的初边值问题。首先,利用Banach压缩映射原理证明了局部解的存在性和唯一性。然后,通过“凹性”方法,我们在情况1):、情况2):和情况3):中为某些解建立了三个爆破结果。最后,我们认为,对于不同的初始能量,给出了爆破时间上界的估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation
In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.
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