degenerate parabolic equation

degenerate parabolic equation的基本解释

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退化抛物[型]方程

与degenerate parabolic equation相关的网络例句 [注：此内容来源于网络，仅供参考]

The second part is the controllability of parabolic equation .We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null-controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control .

第二部分写的是，抛物方程的能控性，我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

As we all know, it is equivalent to the null controllability of a cascade system governedby two linear degenerate parabolic equations. Next, we study the null controllability of acascade system governed by a semilinear degenerate parabolic equation and a semilinear heatequation.

众所周知，这等价于两个线性退化抛物方程构成的耦合系统在单个控制作用下的零能控问题；接下来我们又考虑了一类半线性退化抛物方程与半线性热方程构成的耦合系统的零能控问题。

与degenerate parabolic equation相关的网络解释 [注：此内容来源于网络，仅供参考]

degenerate parabolic equation：退化抛物型方程

degenerate kernel 退化核 | degenerate parabolic equation 退化抛物型方程 | degenerate polyhedron 退化多面体

degenerate parabolic equation：拟线性退缩抛物方程

伪抛物型积分微分方程:Linear Quasi-parabolic Integro-differential Equation | 拟线性退缩抛物方程:Degenerate parabolic equation | 抛物型变分不等式:parabolic variational inequalities

Quasilinear degenerate parabolic equation：拟线性退化抛物方程

大型反射面天线:large parabolic reflector antenna | 拟线性退化抛物方程:Quasilinear degenerate parabolic equation | 要素:element