| 一类非线性高阶Kirchhoff型方程的初边值问题 |
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| 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 |
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| 作者姓名： | 叶耀军 陶祥兴 |
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| 作者单位： | 浙江科技学院数学与信息科学系 杭州 310023 |
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| 基金项目： | 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） |
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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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| 关 键 词： | 非线性高阶Kirchhoff型方程 初边值问题 整体解 衰减估计 解的爆破 |
Initial Boundary Value Problem for Higher-order Nonlinear Kirchhoff-type Equation |
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| Yao Jun YE,Xiang Xing TAO. Initial Boundary Value Problem for Higher-order Nonlinear Kirchhoff-type Equation[J]. Acta Mathematica Sinica, 2019, 62(6): 923-938 |
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| Authors: | Yao Jun YE Xiang Xing TAO |
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| Affiliation: | Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China |
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| Abstract: | In this paper, the initial boundary value problem for some nonlinear higherorder Kirchhoff-type equation with damping and source terms in a bounded domain is studied. We prove the existence of global solutions for this problem by constructing a stable set and establish the energy decay estimate by applying a difference inequality due to Nakao. Meanwhile, under the condition of the positive initial energy, it is shown that the solution blows up in the finite time and the lifespan estimate of solution is also given. |
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| Keywords: | nonlinear higher-order Kirchhoff-type equation initial-boundary value problem global solution decay estimate blow-up |
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