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具有负记忆项的非线性黏弹性方程的初边值问题

The initial boundary value problems for a nonlinear viscoelastic equation with negative memory
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摘要 讨论了具有负记忆项的非线性黏弹性方程uu+△2u+αu-∫g(t-τ)△2u(τ)dτ+β|ut|ρut=0r|u|ξu的初边值问题.通过构造修正位势井,利用Galerkin方法和紧致性原理,得出了整体正则解的存在性和渐近性,并利用能量补偿法证明了解的爆破性. The initial boundary value problems for a nonlinear viscoelastic equation with negative memory tas follow uu＋△2u＋αu-∫^t0 g（t-τ）△2u（τ）dτ＋β｜ut｜ρut=r｜u｜^ξu is discussed. By constructing the modified potential well, applying Galerkin method and compactness principle, the existence and asymptot-ic behavior of global regular solution of these problems are obtained, and the blowup of the solution is proved by making use of the energy compensation method.
作者 辛向军 张宏伟
机构地区 郑州轻工业学院数学与信息科学系 河南工业大学理学院
出处 《郑州轻工业学院学报（自然科学版）》 CAS 2010年第4期107-110,共4页 Journal of Zhengzhou University of Light Industry:Natural Science
基金 河南省基础与前沿技术研究计划项目(092300410045)
关键词 黏弹性方程 初边值问题 负记忆 整体解的存在性 解的渐近性 viscoelastic equation initial boundary value problem negative memory existence of global so-lution asymptotic behavior of solution
分类号 O175.26 [理学—基础数学]
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参考文献10

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二级参考文献14

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郑州轻工业学院学报（自然科学版）
2010年 第4期

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