共查询到20条相似文献,搜索用时 15 毫秒
1.
Xiang-Tuan Xiong Hong-Fang Li 《Journal of Mathematical Analysis and Applications》2006,317(1):331-348
We consider a non-standard inverse heat conduction problem in a quarter plane which appears in some applied subjects. We want to know the surface heat flux in a body from a measured temperature history at a fixed location inside the body. This is an exponentially ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. A Fourier regularization method together with order optimal logarithmic stability estimates is given. A numerical example shows that the theoretical results are valid. 相似文献
2.
In this paper,we introduce a modified Landweber iteration to solve the sideways parabolic equation,which is an inverse heat conduction problem(IHCP) in the quarter plane and is severely ill-posed.We shall show that our method is of optimal order under both a priori and a posteriori stopping rule.Furthermore,if we use the discrepancy principle we can avoid the selection of the a priori bound.Numerical examples show that the computation effect is satisfactory. 相似文献
3.
《Applied Mathematics Letters》2003,16(4):475-479
A wavelet regularization method for a general sideways parabolic equation is given. Some sharp stability estimates are also provided. 相似文献
4.
《Journal of Computational and Applied Mathematics》2004,167(2):449-463
The inverse heat conduction problem (IHCP) can be considered to be a sideways parabolic equation in the quarter plane, and now the results available in the literature on IHCP mainly devoted to the standard sideways heat equation. Numerical methods have been developed also for more general equations, but, in most cases, the stability theory and convergence proofs have not been generalized accordingly. This paper remedies this by a simplified Tikhonov and a new Fourier regularization methods on a general sideways parabolic equation. Some known results for sideways heat equation are only the special case of the conclusions in this paper.The numerical example shows that the computation effect is satisfactory. 相似文献
5.
Chu-Li Fu Xiang-Tuan Xiong Hong-Fang Li You-Bin Zhu 《Applied mathematics and computation》2005,160(3):97
We consider a special sideways parabolic equation which appears in some applied subjects. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper some wavelet and spectral regularization methods for this problem are given. The error estimates are also established respectively. 相似文献
6.
Jin Ru Wang 《数学学报(英文版)》2010,26(10):1981-1992
We consider the problem uxx(x, t) = ut(x, t), 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g(t) is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g(t) can produce a big alteration on its solution (if it exists). We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren't stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1]. 相似文献
7.
We consider an inverse parabolic problem. We prove that the heat radiative coefficient, the initial temperature and a boundary coefficient can be simultaneously determined from the final overdetermination, provided that the heat radiative coefficient is a priori known in a small subdomain. Moreover we establish a stability estimate for this inverse problem. 相似文献
8.
M. I. Ivanchov 《Journal of Mathematical Sciences》1998,88(3):432-436
We establish conditions for unique determination of an unknown source in a parabolic equation for the case of general boundary
conditions and overdetermined conditions.
Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 125–129. 相似文献
9.
RUIHONGXING 《高校应用数学学报(英文版)》1995,10(1):25-34
The nonoxerlapping domain deoomposition method for parabolic partial differential equation on general domain is considered. A kind of domain decomposition that uses the finite element procedure ks given. The problem.over the domains can be implemented on parallel computer. Convergence analysis is also presented. 相似文献
10.
In this paper, we consider the Cauchy problem for the Laplace equation, in a strip where the Cauchy data is given at x = 0 and the flux is sought in the interval 0<x?1. This problem is typical ill-posed: the solution (if it exists) does not depend continuously on the data. We study a modification of the equation, where a fourth-order mixed derivative term is added. Some error stability estimates for the flux are given, which show that the solution of the modified equation is approximate to the solution of the Cauchy problem for the Laplace equation. Furthermore, numerical examples show that the modified method works effectively. 相似文献
11.
We apply a wavelet dual least squares method to a general sideways parabolic equation for determining surface temperature and surface heat flux. Connecting Meyer wavelet bases with a special project method dual least squares method, we can obtain a regularized solution. Meanwhile, order optimal error estimates between the approximate solution and exact solution are proved. 相似文献
12.
Keying Ma Tongjun Sun Danping Yang 《Numerical Methods for Partial Differential Equations》2009,25(5):1167-1194
Parallel Galerkin domain decomposition procedures for parabolic equation on general domain are given. These procedures use implicit Galerkin method in the subdomains and simple explicit flux calculation on the interdomain boundaries by integral mean method or extrapolation method to predict the inner‐boundary conditions. Thus, the parallelism can be achieved by these procedures. These procedures are conservative both in the subdomains and across interboundaries. The explicit nature of the flux prediction induces a time‐step limitation that is necessary to preserve stability, but this constraint is less severe than that for a fully explicit method. L2‐norm error estimates are derived for these procedures. Compared with the work of Dawson and Dupont [Math Comp 58 (1992), 21–35], these L2‐norm error estimates avoid the loss of H?1/2 factor. Experimental results are presented to confirm the theoretical results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
13.
Jay I. Frankel Majid Keyhani Rao V. Arimilli Jayne Wu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):869-888
This paper derives a new integral relationship between heat flux and temperature in a transient, two-dimensional heat conducting
half space. A unified mathematical treatment is proposed that is extendable to higher-dimensional and finite-region geometries.
The analytic expression provides the local heat flux perpendicular to the front surface solely based on an embedded line of
temperature sensors parallel to the surface. The relationship does not require apriori knowledge of the surface boundary condition.
A new sensor strategy is analytically conceived based on the integral relationship for estimating the local, in-depth heat
flux without surface instrumentation. It should further be clarified that the integral relationship requires only knowledge
of the local, in-depth temperature and heating/cooling rate (time rate of change of temperature). The resulting formulation
is mildly ill-posed and either requires digital filtering of the temperature signal to remove high frequency components of
noise or the development of direct heating/cooling rate sensors. This paper (a) develops the new mathematical relationship;
(b) demonstrates that the proposed relationship reduces to well-known (i) one-dimensional results under the appropriate assumptions;
and, (ii) two-dimensional surface results; and, (c) provides a simple numerical example validating the concept. 相似文献
14.
Jay I. Frankel Majid Keyhani Rao V. Arimilli Jayne Wu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,57(2):869-888
This paper derives a new integral relationship between heat flux and temperature in a transient, two-dimensional heat conducting
half space. A unified mathematical treatment is proposed that is extendable to higher-dimensional and finite-region geometries.
The analytic expression provides the local heat flux perpendicular to the front surface solely based on an embedded line of
temperature sensors parallel to the surface. The relationship does not require apriori knowledge of the surface boundary condition.
A new sensor strategy is analytically conceived based on the integral relationship for estimating the local, in-depth heat
flux without surface instrumentation. It should further be clarified that the integral relationship requires only knowledge
of the local, in-depth temperature and heating/cooling rate (time rate of change of temperature). The resulting formulation
is mildly ill-posed and either requires digital filtering of the temperature signal to remove high frequency components of
noise or the development of direct heating/cooling rate sensors. This paper (a) develops the new mathematical relationship;
(b) demonstrates that the proposed relationship reduces to well-known (i) one-dimensional results under the appropriate assumptions;
and, (ii) two-dimensional surface results; and, (c) provides a simple numerical example validating the concept. 相似文献
15.
Santiago Cano-Casanova Julián López-Gómez Kazuhiro Takimoto 《Journal of Differential Equations》2012,252(1):323-343
This paper studies a quasilinear perturbation, through the mean curvature flow operator, of the classical linear heat equation. The mean curvature has the effect of maintaining bounded all classical positive steady-states of the model. 相似文献
16.
A. Ashyralyev 《Ukrainian Mathematical Journal》2011,62(9):1397-1408
We study the boundary-value problem of determining the parameter p of a parabolic equation
v¢(t) + Av(t) = f(t) + p, 0 \leqslant t \leqslant 1, v(0) = j, v(1) = y, v^{\prime}(t) + Av(t) = f(t) + p,\quad 0 \leqslant t \leqslant 1,\quad v(0) = \varphi, \quad v(1) = \psi, 相似文献
17.
An inverse problem for the determination of an unknown spacewise-dependent coefficient in a parabolic equation is considered. The problem is reformulated as a nonclassical parabolic equation along with the initial and boundary conditions. The iterative fixed point projection method is applied to solve the reformulated problem. The comparison analysis of proposed method with a least square method and some numerical examples are presented. 相似文献
18.
Zhong Qi Yin 《数学学报(英文版)》2012,28(12):2373-2394
This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions, in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions. 相似文献
19.
20.
ABSTRACT This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively. 相似文献
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