共查询到20条相似文献,搜索用时 15 毫秒
1.
Berikbol T. Torebek Ramiz Tapdigoglu 《Mathematical Methods in the Applied Sciences》2017,40(18):6468-6479
A class of inverse problems for restoring the right‐hand side of a fractional heat equation with involution is considered. The results on existence and uniqueness of solutions of these problems are presented. 相似文献
2.
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
3.
On a nonlocal problem for the Laplace equation in the unit ball with fractional boundary conditions 下载免费PDF全文
Mokhtar Kirane Berikbol T. Torebek 《Mathematical Methods in the Applied Sciences》2016,39(5):1121-1128
In this paper, we investigate the correct solvability for the Laplace equation with a nonlocal boundary condition in the unit ball. The considered boundary operator is of fractional order. This problem is a generalization of the well‐known Bitsadze–Samarskii problem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution of heat equation with nonlocal boundary and overdetermination conditions is considered. The existence, uniqueness and continuous dependence upon the data are studied. Some considerations on the numerical solution for this inverse problem are presented with the examples. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
5.
In this study, we consider a coefficient problem of a quasi-linear two-dimensional parabolic inverse problem with periodic boundary and integral over determination conditions. We prove the existence, uniqueness and continuously dependence upon the data of the solution by iteration method. Also, we consider numerical solution for this inverse problem by using linearization and the implicit finite-difference scheme. 相似文献
6.
《Mathematical Methods in the Applied Sciences》2018,41(12):4676-4690
We use the priori estimate method to prove the existence and uniqueness of a solution as well as its dependence on the given data of a singular time fractional mixed problem having a memory term. The considered fractional equation is associated with a nonlocal condition of integral type and a Neuman condition. Our results develop and show the efficiency and effectiveness of the energy inequalities method for the time fractional order differential equations with a nonlocal condition. 相似文献
7.
Masaru Ikehata Hiromichi Itou Akira Sasamoto 《Mathematical Methods in the Applied Sciences》2016,39(13):3565-3575
A two dimensional version of a reconstruction problem of an unknown weld on the interface between two electric conductive plates is considered. It is assumed that the two plates have a same known isotropic homogeneous conductivity, and the line where the welding area is located is known. Under these assumptions, an explicit extraction formula of the location of the tips of the welding area on the line from a single set of an electric current density and the corresponding voltage potential on the boundary of the material formed by the plates is given. This result may have possibility of application to quality evaluation of spot welding fixation strength of a lamina. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition 下载免费PDF全文
In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
An inverse problem for a family of two parameters time fractional diffusion equations with nonlocal boundary conditions 下载免费PDF全文
The determination of a space‐dependent source term along with the solution for a 1‐dimensional time fractional diffusion equation with nonlocal boundary conditions involving a parameter β>0 is considered. The fractional derivative is generalization of the Riemann‐Liouville and Caputo fractional derivatives usually known as Hilfer fractional derivative. We proved existence and uniqueness results for the solution of the inverse problem while over‐specified datum at 2 different time is given. The over‐specified datum at 2 time allows us to avoid initial condition in terms of fractional integral associated with Hilfer fractional derivative. 相似文献
10.
Inverse coefficient problem for a second‐order elliptic equation with nonlocal boundary conditions 下载免费PDF全文
Fatma Kanca 《Mathematical Methods in the Applied Sciences》2016,39(11):3152-3158
In this research article, the inverse problem of finding a time‐dependent coefficient in a second‐order elliptic equation is investigated. The existence and the uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finite‐difference scheme combined with an iteration method are presented, and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
Mokhtar Kirane Salman A. Malik Mohammed A. Al‐Gwaiz 《Mathematical Methods in the Applied Sciences》2013,36(9):1056-1069
We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L2[(0,1) × (0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
V. L. Kamynin 《Mathematical Notes》2005,77(3-4):482-493
We study the unique solvability of the inverse problem of determining the righthand side of a parabolic equation whose leading coefficient depends on both the time and the spatial variable under an integral overdetermination condition with respect to time. We obtain two types of condition sufficient for the local solvability of the inverse problem as well as study the so-called Fredholm solvability of the inverse problem under consideration.Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 522–534.Original Russian Text Copyright © 2005 by V. L. Kamynin.This revised version was published online in April 2005 with a corrected issue number. 相似文献
13.
Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions 总被引:1,自引:0,他引:1
We formulate and analyze a Crank-Nicolson finite element Galerkin method and an algebraically-linear extrapolated Crank-Nicolson method for the numerical solution of a semilinear parabolic problem with nonlocal boundary conditions. For each method, optimal error estimates are derived in the maximum norm.Dedicated to Professor J. Crank on the occasion of his 80th birthdaySupported in part by the National Science Foundation grant CCR-9403461.Supported in part by project DGICYT PB95-0711. 相似文献
14.
This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously. 相似文献
15.
Existence and uniqueness results for a fractional two‐times evolution problem with constraints of purely integral type 下载免费PDF全文
Said Mesloub 《Mathematical Methods in the Applied Sciences》2016,39(6):1558-1567
This paper deals with a fractional two‐times evolution equation associated with initial and purely boundary integral conditions. The existence and uniqueness of generalized solution are proved. The classical functional method based on a priori estimates and density used by many authors in the case of nonfractional differential equations is applied for the time fractional case. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
16.
17.
18.
The Bitsadze–Samarskii type nonlocal boundary value problem for the differential equation in a Hilbert space H with the self‐adjoint positive definite operator A with a closed domain D(A) ? H is considered. Here, f(t) be a given abstract continuous function defined on [0,1] with values in H, φ and ψ be the elements of D(A), and λj are the numbers from the set [0,1]. The well‐posedness of the problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained. The fourth order of accuracy difference scheme for approximate solution of the problem is presented. The well‐posedness of this difference scheme in difference analogue of Hölder spaces is established. For applications, the stability, the almost coercivity, and the coercivity estimates for the solutions of difference schemes for elliptic equations are obtained. Mathematical Methods in the Applied Sciences. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
19.
Abdollah Shidfar Reza Zolfaghari 《Numerical Methods for Partial Differential Equations》2011,27(6):1584-1598
In this article, an inverse problem of determining an unknown time‐dependent source term of a parabolic equation is considered. We change the inverse problem to a Volterra integral equation of convolution‐type. By using Sinc‐collocation method, the resulting integral equation is replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number and the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some examples are given to demonstrate the computational efficiency of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1584–1598, 2010 相似文献
20.
A. V. Glushak 《Mathematical Notes》2007,82(5-6):596-607
We study the relationship between the solutions of abstract differential equations with fractional derivatives and their stability with respect to the perturbation by a bounded operator. Besides, we obtain representations for the solution of an inhomogeneous equation and for an equation containing a fractional power of the generator of a cosine operator function. 相似文献