共查询到20条相似文献,搜索用时 78 毫秒
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热传导反问题中非线性热源的存在性 总被引:2,自引:0,他引:2
研究热传导方程在一类非局部时间的边界条件下线性热源的反演问题。文中应用Sobolev紧性方法证明了热源在Hoelder空间中的(关于时间的)局部存在性。 相似文献
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关于一类色散型发展方程反问题的一个注记宋守根(中南工业大学地质系,长沙410083)文献[1]利用C0半群理论研究一类非线性色散型方程的反问题.其中n是R”中具有光滑边界off的有界区域,面是n维Laplace算子,而算子L0为本文将改进[1]的一个... 相似文献
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一类非单调算法的收敛性质 总被引:2,自引:0,他引:2
1.搜索步长和搜索方向对于无约束最优化问题(?)f(x),其中f:R~n→R~1,f∈C~1,一般采用形如x_(k+1)=x_k+λ_kd_k(k=1,2,…)的迭代算法来求解,这里λ_k为搜索步长,d_k为搜索方向. 相似文献
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一类约束优化问题的非单调信赖域算法 总被引:1,自引:0,他引:1
本文就一类等式约束优化问题,结合当前比较流行的非单调技术,提出了一类新的求解等式约束优化的非单调信赖域算法.其非单调程度由算法自适应控制,计算预测下降量和实际下降量的比值时,采用前m(k)个点的信息,这不同于以前在计算预测下降量和实际下降量的比值时,仅仅采用当前-个点的信息.在没有正则性条件的假设下我们证明了算法是有定义的.并且通过对不同情况的讨论证明了算法的全局收敛性.基本的数值试验表明算法是有效的,且说明提出的非单调信赖域算法比单调信赖域算法有效. 相似文献
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本文从反问题的角度讨论了修订直接消耗系数的几种优化方法,通过引入“投入产出反问题”的概念,建立了拉格朗日优化,二次规划,熵优化等三个优化模型,同时给出了算法和算例,并且比较了各种方法的计算结果。 相似文献
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一类优化问题的非单调信赖域算法 总被引:1,自引:0,他引:1
本文提出了一类带不等式约束和简单边界的非线性优化问题的非单调信赖域算法,在一定的条件下,证明了算法的全局收敛性,并通过数值实验验证了算法的合理性。 相似文献
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一类非线性单调型问题的平行化算法许学军,蒋美群(苏州大学数学系)MRALLELALGORITHMSFORANONLINEARMONOTONEPROBLEM¥XuXue-jun;JiangMei-qun(SuzhouUniversity,Suzhou)... 相似文献
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对称次反对称矩阵的一类反问题 总被引:9,自引:1,他引:9
1 引言 用R~(m×n),SR~(n×n),ASR~(n×n),OR~(n×n)分别表示所有m×n实矩阵,n阶实对称矩阵,n阶实反对称矩阵和n阶实正交矩阵组成的集合,I_k表示k阶单位矩阵,S_k表示k阶反序单位矩阵,||A||表示矩阵A的Frobenius范数。若A=(a_(ij))∈R~(n×n),记D_A=diag(a_(11),a_(22),…,a_(nn)),L_A=(l_(ij))∈R_(n×n)其中当i>j时,l_(ij)=a_(ij),当i≤j时,l_(ij)=0,(i,j=1,2,…,n).若A=(a_(ij)),B=(b_(ij))∈R~(m×n),A*B表示A与B的Hadamard乘积,其定义为A*B=(a_(ij)b_(ij))。 相似文献
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We consider the problem of identifying a nonlinear heat transfer law at the boundary, or of the temperature-dependent heat transfer coefficient in a parabolic equation from boundary observations. As a practical example, this model applies to the heat transfer coefficient that describes the intensity of heat exchange between a hot wire and the cooling water in which it is placed. We reformulate the inverse problem as a variational one which aims to minimize a misfit functional and prove that it has a solution. We provide a gradient formula for the misfit functional and then use some iterative methods for solving the variational problem. Thorough investigations are made with respect to several initial guesses and amounts of noise in the input data. Numerical results show that the methods are robust, stable and accurate. 相似文献
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Jennifer Zhao Weizhong Dai Tianchan Niu 《Numerical Methods for Partial Differential Equations》2007,23(5):949-959
In this article, a set of fourth‐order compact finite difference schemes is developed to solve a heat conduction problem with Neumann boundary conditions. It is derived through the compact difference schemes at all interior points, and the combined compact difference schemes at the boundary points. This set of schemes is proved to be globally solvable and unconditionally stable. Numerical examples are provided to verify the accuracy.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
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Ebru Ozbilge 《Applicable analysis》2013,92(12):1931-1938
This article deals with boundary-value problems (BVPs) for the second-order nonlinear differential equations with monotone potential operators of type Au := ??(k(|?u|2)?u(x)) + q(u 2)u(x), x ∈ Ω ? R n . An analysis of nonlinear problems shows that the potential of the operator A as well as the potential of related BVP plays an important role not only for solvability of these problems and linearization of the nonlinear operator, but also for the strong convergence of solutions of corresponding linearized problems. A monotone iterative scheme for the considered BVP is proposed. 相似文献
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王明新 《中国科学A辑(英文版)》2003,46(2):169-175
This paper deals with the blow-up rate estimates of positive solutions for systems of heat equations with nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained. 相似文献
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§1IntroductionInthispaper,weconsiderthelargetimebehaviorofaproblem,ut=Δu+up,x∈RN+,t>0,-ux1=uq,x1=0,t>0,u(x,0)=u0(x),x∈RN+,(... 相似文献
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Mansur I. Ismailov Bülent Oğur 《Numerical Methods for Partial Differential Equations》2016,32(2):564-590
This article considers the inverse problem of identification of a time‐dependent thermal diffusivity together with the temperature in an one‐dimensional heat equation with nonlocal boundary and integral overdetermination conditions when a heat exchange takes place across boundary of the material. The well‐posedness of the problem is studied under some regularity, and consistency conditions on the data of the problem together with the nonnegativity condition on the Fourier coefficients of the initial data and source term. The inverse problem is also studied numerically by using the Crank–Nicolson finite difference scheme combined with predictor‐corrector technique. The numerical examples are presented and discussed. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 564–590, 2016 相似文献
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Yong-ping Sun 《高校应用数学学报(英文版)》2008,23(4):413-419
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method. 相似文献
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TANGWEIJUN 《高校应用数学学报(英文版)》1997,12(4):427-440
In this paper, a new method of boundary reduction is proposed, which reduces thesteady-state heat transfer equation with radiation. Moreover, a boundary element method is pre-sented for its solution and the error estimates of the numerical approximations are given. 相似文献
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Andrey E. Kovtanyuk Alexander Yu. Chebotarev Nikolai D. Botkin Karl-Heinz Hoffmann 《Journal of Mathematical Analysis and Applications》2014
Conductive–convective–radiative heat transfer in a scattering and absorbing medium with reflecting and radiating boundaries is considered. The P1 approximation (diffusion model) is used for the simplification of the original problem. The existence of bounded states of the diffusion model is proved. The uniqueness of solutions is established under certain assumptions. 相似文献
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研究了一类带不定权非线性边界的p-Laplacian椭圆方程.获得了当非线性边界的特征值参数小于第二特征值时,该方程存在非平凡解.主要工具为环绕定理. 相似文献