共查询到20条相似文献,搜索用时 15 毫秒
1.
We study solvability of inverse problems of finding the right-hand side together with a solution itself for vector-valued
parabolic and elliptic equations. The usual boundary conditions are supplemented with the overdetermination conditions that
are the values of a solution on some system of surfaces. 相似文献
2.
We consider the problem of simultaneously determining coefficients of a second order nonlinear parabolic equation and a solution to this equation. The unknown coefficients occur in the main part and in the nonlinear summand as well. The overdetermination conditions are conditions of the Dirichlet type on a family of planes of arbitrary dimension. It is demonstrated that the problem in question is solvable locally in time in Hölder spaces. When the unknown functions enter the right-hand side and the equation is linear, the theorem of global unique existence (in time) is established. 相似文献
3.
4.
S. G. Pyatkov 《Journal of Applied and Industrial Mathematics》2011,5(3):417-430
Under study are the inverse problems of determining the right-hand side of a particular form and the solution for elliptic
systems, including a series of elasticity systems. (On the boundary of the domain the solution satisfies either the Dirichlet
conditions or mixed Dirichlet-Neumann conditions.) We assume that on a system of planes the normal derivatives of the solution
can have discontinuities of the first kind. The conjugating boundary conditions on the discontinuity surface are analogous
to the continuity conditions for the fields of displacements and stresses for a horizontally laminated medium. The overdetermination
conditions are integral (the average of the solution over some domain is specified) or local (the values of the solution on
some lines are specified). We study the solvability conditions for these problems and their Fredholm property. 相似文献
5.
S. A. Tersenov 《Siberian Mathematical Journal》2010,51(2):338-345
Considering forward-backward parabolic equations we pose and study some problems of the Cauchy type. 相似文献
6.
7.
Mathematical Notes - 相似文献
8.
S. G. Pyatkov 《Journal of Mathematical Sciences》2008,150(5):2422-2433
In the paper, we study the inverse problem of finding the solution u and the coefficient q from the following data:
where G ⊂ ℝn is a bounded domain with boundary Γ and L is a second-order elliptic operator. We prove that the problem is locally solvable in time or in the case where the norms
of its data are sufficiently small.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 187–202, 2006. 相似文献
9.
Alemdar Hasanov Ali Demir Arzu Erdem 《Journal of Mathematical Analysis and Applications》2007,335(2):1434-1451
This article presents a mathematical analysis of input-output mappings in inverse coefficient and source problems for the linear parabolic equation ut=(kx(x)ux)+F(x,t), (x,t)∈ΩT:=(0,1)×(0,T]. The most experimentally feasible boundary measured data, the Neumann output (flux) data f(t):=−k(0)ux(0,t), is used at the boundary x=0. For each inverse problems structure of the input-output mappings is analyzed based on maximum principle and corresponding adjoint problems. Derived integral identities between the solutions of forward problems and corresponding adjoint problems, permit one to prove the monotonicity and invertibility of the input-output mappings. Some numerical applications are presented. 相似文献
10.
11.
A. Y. Akhundov 《Ukrainian Mathematical Journal》2006,58(1):127-138
The questions of well-posedness and approximate solution of inverse problems of finding unknown functions on the right-hand
side of a system of parabolic equations are investigated. For the problems considered, theorems on the existence, uniqueness,
and stability of a solution are proved and examples that show the exactness of the established theorems are given. Moreover,
on the set of well-posedness, the rate of convergence of the method of successive approximations suggested for the approximate
solution of the given problems is estimated.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 115–124, January, 2006. 相似文献
12.
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients. 相似文献
13.
14.
15.
16.
V. L. Kamynin 《Mathematical Notes》2008,84(1-2):45-54
We study the unique solvability of the inverse problem of determining the leading coefficient in the parabolic equation on the plane with coefficients depending on both time and spatial variables under the condition of integral overdetermination with respect to time. We obtain sufficient conditions for the unique solvability of the inverse problem. We present nontrivial examples of problems for which such conditions hold. It is shown that the imposed conditions necessarily hold if either the time interval is sufficiently large or the space interval on which the problem is considered is sufficiently small. 相似文献
17.
John R. Cannon Hong-Ming Yin 《Numerical Methods for Partial Differential Equations》1990,6(2):177-191
In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we introduce a variational form by defining a new function. Both continuous and discrete Galerkin procedures are illustrated in this paper. The error estimates are also derived. 相似文献
18.
Yu. S. Éidel'man 《Ukrainian Mathematical Journal》1993,45(1):132-140
Necessary and sufficient conditions are established for the unique solvability of problems of determining an unknown right-hand side of a differential equation with an unbounded operator coefficient under an additional boundary condition.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 120–127, January, 1993. 相似文献
19.
S. N. Kruzhkov 《Mathematical Notes》1969,6(3):634-637
Theorems are established concerning the solubility in the large of the Cauchy problem for quasi-linear parabolic second-order equations.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 295–300, September, 1969. 相似文献