共查询到20条相似文献,搜索用时 15 毫秒
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We study the backward problem for non-linear (semilinear) parabolic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new Fourier truncated regularization method for stabilising the ill-posed problem. In comparison with previous studies on solving the nonlinear backward problem, our method shows a significant improvement. 相似文献
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Fatma Gamze Düzgün Kamal Nasir Soltanov 《Journal of Applied Analysis & Computation》2014,4(3):271-281
In this paper, some mixed problem with third type boundary value for a semilinear parabolic equation is investigated. Here the solvability theorems for considered problem and the uniqueness theorem for a model case of the problem are showed. 相似文献
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半线性抛物型积分—微分方程的谱方法 总被引:1,自引:0,他引:1
本文在讨论带有半线性记忆项抛物型方程半离散格式的基础上,构造了空间方向谱离散,时间方向后欧拉方法的全离散格式,并给出了误差估计。对于记忆项的数值积分,采用了梯形公式与矩形公式结合的方法,并估计了数值积分的影响。 相似文献
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Francesco Ludovici Ira Neitzel Winnifried Wollner 《Journal of Optimization Theory and Applications》2018,178(2):317-348
We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In order to control the feasibility violation induced by the discretization, error estimates for the semilinear partial differential equation are derived. Based upon these estimates, it can be shown that any local minimizer of the semilinear parabolic optimization problems satisfying a weak second-order sufficient condition can be approximated by the discretized problem. Rates for this convergence in terms of temporal and spatial discretization mesh sizes are provided. In contrast to other results in numerical analysis of optimization problems subject to semilinear parabolic equations, the analysis can work with a weak second-order condition, requiring growth of the Lagrangian in critical directions only. The analysis can then be conducted relying solely on the resulting quadratic growth condition of the continuous problem, without the need for similar assumptions on the discrete or time semidiscrete setting. 相似文献
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Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations 总被引:2,自引:0,他引:2
In this paper we study optimal control problems governed by semilinear parabolic equations. We obtain necessary optimality
conditions in the form of an exact Pontryagin's minimum principle for distributed and boundary controls (which can be unbounded)
and bounded initial controls. These optimality conditions are obtained thanks to new regularity results for linear and nonlinear
parabolic equations.
Accepted 17 March 1997 相似文献
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丁俊堂 《数学物理学报(A辑)》2004,24(1):63-70
文中构造了一类具有Dirichlet或Neumann边界条件的半线性抛物方程u_t=Δu+f(x,u,q,t) (q=|u|^2)的解的一个辅助函数,对其使用Hopf最大值原理和黎曼几何理论,从而获得了该函数的最大值原理,据此原理获得了梯度q和解u的估计. 相似文献
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作为飞机环控系统与主发动机起动的气源,以目前广泛应用的带负载压气机结构APU(Auxiliary Power Unit)为研究对象,进行引气特性计算模型与计算方法研究。首先介绍了APU结构与引气工作特点,然后分析了建模时喘振控制阀SCV(Surge Control Valve)控制方法与APU共同工作机理,最后采用部件法建立了该类型APU引气计算数学模型。以某型APU为对象进行数值仿真并与实际试车数据比较,计算误差小于3%,表明所采用的建模方法是正确的,所建立的模型能够满足工程需求。 相似文献
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We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different
methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem.
Accepted 10 June 1996 相似文献
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In this paper we prove the internal feedback stabilization of steady-state solutions of semilinear parabolic equations and introduce a controller synthesis methodology based on finite element approximations of the original PDEs. Numerical tests are given for some one- and two-dimensional nonlinear parabolic equations. 相似文献
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Hans D. Mittelmann 《Computational Optimization and Applications》2001,20(1):93-110
We study optimal control problems for semilinear parabolic equations subject to control constraints and for semilinear elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes, the parabolic one with boundary control and the elliptic one with boundary or distributed control, are discretized by a finite difference method. The discrete SSC are stated and numerically verified in all cases providing an indication of optimality where only necessary conditions had been studied before. 相似文献
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Boya Zhou & Dongfang Li 《高等学校计算数学学报(英文版)》2020,13(4):928-945
In this study, Newton linearized finite element methods are presented for
solving semi-linear parabolic equations in two- and three-dimensions. The proposed
scheme is a one-step, linearized and second-order method in temporal direction,
while the usual linearized second-order schemes require at least two starting values. By using a temporal-spatial error splitting argument, the fully discrete scheme
is proved to be convergent without time-step restrictions dependent on the spatial
mesh size. Numerical examples are given to demonstrate the efficiency of the methods and to confirm the theoretical results. 相似文献
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Mingxin Wang 《偏微分方程(英文版)》1995,8(3):273-280
This paper deals with the following semilinear parabolic equations with nonlinear boundary conditions u_t - Δu = f(u) - λu,x ∈ Ω, t > 0 \frac{∂u}{∂n} = g(u), \qquad x ∈ ∂Ω, t > 0 It is proved that every positive equilibrium solution is a threshold. 相似文献
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X. J. Yu 《计算数学(英文版)》1996,14(4):363-382
1.IntroductionThefiniteelementmethodsforsolvingnonlinearparabolicproblemsarestudiedbymanyauthors,suchasDouglasandDupont[5],Wheelerl4],Luskin[3lfetc.Theyproposedvariouswaysofcomputingtheproblemsandprovedtheoptimalorderconvergenceratesofthemethods,suchasthelinearizedmethods,thepredictor-correctormethods,theextraPolationmethods,thealternatingdirectiollmethodsandtheiterativemethodsl2]1etc.Themultigridmethodsforsolvingparabolicproblemsarestudiedbysomeauthors,suchasHachbuschl14,15],BankandDupontl… 相似文献