parabolic differential equation

parabolic differential equation的基本解释

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抛物线微分方程

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抛物型微分方程

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

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

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。

Chapter 3 emphasizes on the case that the considered systems contain not only impulse but also time delay. We mainly investigate impulsive parabolic systems with time delay and neutral impulsive parabolic systems. Section 3.1 discusses the oscillation of impulsive parabolic systems with time delay under Robin boundary condition and obtains some useful criteria via first order impulsive differential inequalities with time delay. Section 3.2 studies the oscillation of neutral impulsive parabolic systems under Neumann boundary condition and Robin boundary condition, respectively, and obtains some sufficient conditions for oscillation and strong oscillation via first order neutral impulsive differential inequalities.

第三章针对于"脉冲"与"时滞"共存的复杂情形，仍采用反证法讨论了含时滞的脉冲偏微分系统的振动理论，具体研究了脉冲时滞抛物系统和中立型脉冲时滞抛物系统。3.1节考虑了脉冲时滞抛物系统的振动理论，借助于一阶脉冲时滞微分不等式的解的性质，得到了满足Robin边界条件的脉冲时滞抛物系统的若干振动准则；3.2节考虑了中立型脉冲时滞抛物系统的振动理论，借助于一阶中立型脉冲时滞微分不等式的解的性质，分别给出了满足Neumann边界条件和Robin边界条件的中立型脉冲时滞抛物系统的若干振动和强振动准则。

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

parabolic differential equation：抛物型微分方程

parabolic cylinder function 抛物柱面函数 | parabolic differential equation 抛物型微分方程 | parabolic folium 抛物叶形线

parabolic differential equation：拋物线微分方程式

拋物線近似 parabolic approximation | 拋物線微分方程式 parabolic differential equation | 拋物線反射器 parabolic dish

parabolic partial differential equation：抛物型偏微分方程

抛物度量群 parabolic metric group | 抛物型偏微分方程 parabolic partial differential equation | 抛物型点 parabolic point

parabolic partial differential equation：抛物型偏微分方程,抛物型微分方程

parabolic orbit 抛物线轨道 | parabolic partial differential equation 抛物型偏微分方程,抛物型微分方程 | parabolic plane 抛物平面

partial differential equation of parabolic type：抛物型偏微分方程

partial differential equation of mixed type 混合型偏微分方程 | partial differential equation of parabolic type 抛物型偏微分方程 | partial differential operator 偏微分算子