Kirchhoff方程论文：Kirchhoff方程 Faedo-Galerkin方法 存在性 唯一性 衰减性.docVIP

【关键词】Kirchhoff方程 Faedo-Galerkin方法 存在性 唯一性 衰减性 【英文关键词】Kirchhoff equation Faedo-Galerkin method The existence Theuniqueness Uniform decay Kirchhoff方程论文：带有声学边界条件的非线性粘弹性Kirchhoff方程解的存在性与一致衰减性 【中文摘要】本文研究非线性粘弹性Kirchhoff方程在声学边界条件下解的存在性,唯一性与一致衰减性.本文共分五节第一节,介绍了非线性粘弹性Kirchhoff方程的研究意义及国内外研究现状,同时给出本文所要研究问题的假设条件.第二节,列出Sobolev嵌入定理和几个重要的不等式等预备知识.第三节,证明了(1.1)-(1.4)解的存在性与唯一性,其中包括Faedo-Galerkin逼近,先验估计,极限过程以及解的唯一性四个部分.第四节,在适当的假设下,我们将证明来得出解的一致衰减性.第五节,在适当的假设下,我们通过引入下面的泛函其中ε,μ为正常数并且证明解的一致衰减性, 【英文摘要】This paper is concerned with the existence, the uniqueness and the uniform decay for the solution of the following viscoelastic Kirchhoff-type equation with acoustic boundary conditions,This dissertation is divided into five sections.In the first section, we introduce the importance and the international re-search progress of the nonlinear viscoelastic Kirchhoff-type equation, we also state the hypotheses for the problem.In the second section, we list some preliminaries such as the Sobolev imbed-ding theorem, several kinds of important inequalities and so on.In the third section, we prove the existence and the uniqueness of the solution to the problem (1.1)-(1.4). The proof of the existence includes Faedo-Galerkin approximation, some prior estimates, limiting process.In the forth section, under suitable conditions, we prove the uniform decay of the solution: In the fifth section, under suitable conditions, we prove the uniform decay of the solution: by implying the functional where ε,μ are arbitrary positive constants, and the definitions of F(t),Φ(t) are given by 【目录】带有声学边界条件的非线性粘弹性Kirchhoff方程解的存在性与一致衰减性 摘要 4-6 Abstract 6-7 第一节 引言 9-13 第二节 预备知识 13-17 第三节 解的存在性与唯一性 17-31 第四节 解的一致衰减性(Ⅰ) 31-48 第五节 解的一致衰减性(Ⅱ) 48-58 参考文献 58-61 致谢 61