一类非线性高阶Kirchhoff型方程的初边值问题

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一类非线性高阶Kirchhoff型方程的初边值问题叶耀军, 陶祥兴浙江科技学院数学与信息科学系杭州 310023 Initial Boundary Value Problem for Higher-order Nonlinear Kirchhoff-type Equation Yao Jun YE, Xiang Xing TAODepartment of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China

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摘要本文研究了一类具有非线性耗散项的高阶Kirchhoff型方程的初边值问题．通过构造稳定集讨论了此问题整体解的存在性，应用Nakao的差分不等式建立了解能量的衰减估计．在初始能量为正的条件下，证明了解在有限时间内发生blow-up，并且给出了解的生命区间估计．

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收稿日期: 2016-11-16

MR (2010):

O175.2

基金资助:国家自然科学基金（61273016，11171306，11571306）；浙江省自然科学基金（LY17A010009）；浙江省科技厅公益性技术应用研究课题资助项目（2015C33088）

作者简介: 叶耀军,E-mail:yjye2013@163.com;陶祥兴,E-mail:xxtau@163.com

引用本文:

叶耀军, 陶祥兴. 一类非线性高阶Kirchhoff型方程的初边值问题[J]. 数学学报, 2019, 62(6): 923-938. Yao Jun YE, Xiang Xing TAO. Initial Boundary Value Problem for Higher-order Nonlinear Kirchhoff-type Equation. Acta Mathematica Sinica, Chinese Series, 2019, 62(6): 923-938.

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