具有记忆的非齐次MGT方程的研究

发布时间：2018-06-29 12:10

本文选题：粘性波动方程 + 非齐次方程　；参考：《曲阜师范大学》2017年硕士论文

【摘要】：考虑具有记忆项的非齐次Moore-Gibson-Thompson (MGT)方程:τuttt+αutt+c2Au+bAut-∫0tg(t-s)Au(s)ds =|u|pu,本文主要在Hilbert空间中研究具有记忆的非齐次Moore-Gibson-Thompson方程的能量衰减问题,在对初值及记忆核函数等的合适假设下,我们证明能量泛函的衰减速率取决于记忆核函数的衰减性质.本论文的证明具体分为三步:第一步,用乘子方法构造方程的能量泛函E(t),通过对R(t)的估计由d/dt,E(t)=-R(t)得到能量泛函E(t)的初步衰减估计;第二步,构造能量泛函E(t)的等价泛函H(t);第三步,用微分法和积分法分别对能量泛函E(t)衰减估计,证得当记忆核函数以指数形式衰减时能量泛函E(t)也以指数形式衰减.本文证明了当记忆核函数以指数形式衰减时,具有记忆的非齐次MGT方程也以指数形式衰减.
[Abstract]:In this paper, we consider the inhomogeneous Moore-Gibson-Thompson (MGT) equation with memory term: 蟿 uttt 伪 utt c2Au bAut- 0tg (t-s) Au (s) ds = 0tg). In this paper, we study the energy decay problem of nonhomogeneous Moore-Gibson-Thompson equation with memory in Hilbert space. We prove that the decay rate of the energy functional depends on the attenuation property of the memory kernel function. The proof of this paper is divided into three steps: in the first step, the energy functional E (t), of the equation is constructed by means of the multiplier method. The initial decay estimate of the energy functional E (t) is obtained from the estimation of R (t) by D / DT (t) (t) R (t), and the third step is to construct the equivalent functional H (t); of the energy functional E (t). The energy functional E (t) attenuation is estimated by the differential method and the integral method respectively. It is proved that the energy functional E (t) attenuates exponentially when the memory kernel function attenuates exponentially. In this paper, it is proved that when the memory kernel function attenuates exponentially, the inhomogeneous MGT equation with memory also attenuates exponentially.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【相似文献】