项目名称: 膜状极化材料的偏微分方程模型的适定性分析
项目编号: No.11471126
项目类型: 面上项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 杜毅
作者单位: 暨南大学
项目金额: 60万元
中文摘要: 本项目将研究膜状(Thin-domain)极化材料的偏微分方程模型.此类型材料在工业生产中有广泛的应用,例如压电陶瓷,液晶,聚偏氟乙烯高分子聚合物等,是目前材料生产及结构分析中受到广泛关注的领域.与此同时其对应的偏微分方程模型在结构上耦合了几类偏微分方程的研究热点问题.确切来讲,根据介质特征通过对其模型中参数的选取,对应的偏微分方程模型可粗略看作为麦克斯韦方程组耦合弹性力学方程组(固态材料)或麦克斯韦方程组耦合粘弹性流体力学方程组(复杂流体材料).本项目将研究以上两类耦合型方程组.对于刻画纯固态材料的方程组我们将研究其对应的弹性波的传播特征,分析小初值经典解的生命跨度、外问题的零条件结构,及解的奇性形成机制等;对于粘弹性流体材料的方程组,我们将研究在膜状区域上部分粘性时解的适定性,粘性消失时对应的边界层理论以及无粘性时的奇性形成.
中文关键词: 极化材料;膜;偏微分方程模型;适定性
英文摘要: In this proposal, we shall study the well-posedness for the PDE model to piezoelectricity material on a thin-domain. The piezoelectricity material have many applications in industry. Besides, its PDE model have coupled some different type of PDE equations, which are hot topics in theory reasearch. More precisely, by choosing the parameter in the PDE model, the PDE model can be regard as a coupled system of elasticity and Maxwell equations (the solid case) or visco-elasticity coupled a Maxwell equations (the complex fluid case). In case of solid piezoelectricity material, we shall study the wave propagation property, the lifespan to the small smooth solutions to the Cauchy problem, the null conditions, and also the singularity formation. Meanwhile, we also study the visco-elasticity case on a thin-domain. We shall study the well-posedness of the solutions with partial viscocity, the prandtl's system when the viscocity disappear, and the singularity formation of the local solutions. Finally, we shall also present some numerical simulation for the systems.
英文关键词: Piezoelectricity Material;Thin-Domain;Partial differential equations model;well-posedness