抛物型偏微分方程
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In this paper we will study the uniqueness of weak solutions of the first boundary value problem for a degenerate parabolic equation.
本文研究了一类具有退化性的抛物型偏微分方程的第一边值问题的弱解的唯一性。
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Aimed to the differential equation in form of convolution and the functional presented by M. E. Gurtin, the matrix operator which includes the differential equation and the boundary condition is proved self-adjoint, furthermore a general variational principles in form of convolution and the preparation theorem are given and proved.
针对M.E.Gurtin提出的含卷积运算的抛物型偏微分方程及其对应的泛函，运用泛函势算子理论，从理论上证明了含卷积运算的抛物型偏微分方程及其边界条件所对应的矩阵算子有势，进而给出并证明了具有普适意义的含卷积运算的变分定理及预备定理。
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This paper gives the probabilistic interpretation for one system of the second order quasilinear parabolic partial differential equations combined with an algebra equation using fully coupled forward-backward stochastic differential equation.
本文利用完全耦合的正倒向随机微分方程，对一类耦合了一个代数方程的二阶拟线性抛物型偏微分方程系统，给出概率表示。
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In this paper, we used the regularization method and the best disturbed iteration to solve such more extensive equations: every kind of positive problems and inverse problems of the hyperbolic partial differential equation and parabolic equation. We give homologous methods to solve the positive problems and inverse problems of nonlinear Burgers equation and Boussinesq equation.
本文应用正则化方法和最佳摄动量法，解决了一类更广泛的双曲型和抛物型偏微分方程的各类正问题及反问题，对非线性的Burgers方程及Boussinesq方程的正问题及反问题，也给出了相应的求解方法。
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This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.
本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。
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The partial differential equations with singular coefficients are very important ones in the field of numerical mathematics.
摘要具有奇异系数的椭圆及抛物型偏微分方程是一类很重要的方程，早在二十世纪六十年代左右，许多的计算数学工作者就开始研究此类方程的数值方法及相应的数学理论。
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The models of American option and perpetual American option are a free boundary problem of parabolic partial differential equation and ordinary differential equation respectively.
在相应的基本假设下，美式期权的定价模型是一个抛物型偏微分方程自由边界问题，而永久美式期权的定价模型是一个常微分方程自由边界问题。
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The parabolic partial differential equation is an important type of mathematical physical equations. It can describe the problems of heat conduction, seepage flow and diffusion, et al.
抛物型偏微分方程是描述热传导、渗流、扩散等过程的一类重要的数学物理方程。
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Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.
其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。
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Stratum hurting ; parabolic partial different equation ; difference equation
地层伤害；抛物型偏微分方程；差分方程
- 更多网络解释与抛物型偏微分方程相关的网络解释 [注：此内容来源于网络，仅供参考]
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partial differential operator：偏微分算子
partial differential equation of parabolic type 抛物型偏微分方程 | partial differential operator 偏微分算子 | partial differentiation 偏微分法
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partial differential equation of mixed type：混合型偏微分方程
partial differential equation of hyperbolic type 双曲型偏微分方程 | 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
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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
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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
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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
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parabolic point：抛物型点
抛物型偏微分方程 parabolic partial differential equation | 抛物型点 parabolic point | 抛物性射影 parabolic projectivity