Coefficient In Parabolic Equation Research Articles

Numerical procedure for the determination of an unknown coefficients in parabolic equations

A numerical procedure for an inverse problem of determination of unknown coefficients in a class of parabolic differential equations is presented. The approach of the proposed method is to approximate unknown coefficients by a piecewise linear function whose coefficients are determined from the solution of minimization problem based on the overspecified data. Some numerical examples are presented.

On determination of a time-dependent leading coefficient in a parabolic equation

N. I. Ivanchov UDC 517.95 In the present article, we study the question of the influence of lower-order terms on the possibil- ity of unique determination of the time-depending leading coefficient of a one-dimensionM parabolic equation. We establish that the conditions for existence and uniqueness of a solution to the problem differ from the corresponding conditions for the equation without lower-order terms only in some as- sumptions on the lower-order terms and possible decrease of the time interval on which the solution is determined. A similar problem for a coefficient depending on the space variable was considered in [1, 2]. Various statements of inverse problems on determination of leading coefficients in parabolic equations without lower-order terms were studied in [3-6]. Let

On the identification of coefficients of semilinear parabolic equations

In this paper, a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered. General theorems on existence are proved inL1 setting. A necessary condition is given for the solution of the parameter estimation problem.

Identification of Discontinuous Parameters in Flow Equations

A problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered. General theorems on existence and convergence of Galerkin approximations are proved in $L^1 $ setting. Classes of functions of bounded variation are discussed and the variation estimates are obtained. A double-discretization method with the variations constraints is used in two- and three-dimensional problems and the numerical experiments are presented.

Error Estimation for Determination of Unknown Coefficients in Parabolic Equations

We analyze a direct numerical method for the parameter identification problem of the one-dimensional parabolic equation. The method is based on a "Space Marching" idea while we use the hyperbolic perturbation to stabilize the computation. Using the "Space Marching" technique, the parameter identification problem can be solved without any iterative procedure. An error estimate is obtained in the energy norm.

Explicit solutions of certain multidimensional inverse problems for systems of parabolic-type equations

Explicit solutions have been found for inverse problems of determining the system coefficients of parabolic equations, where the unknown coefficients are functions of time and space variables. The results of numerical calculations are given.

Optimal control in coefficients for weak variational problems in Hilbert space

In this paper we give sufficient conditions for the existence of solutions of a problem of parametric optimization. We use continuity with respect to a functional parameter of weak solutions of a variational problem in a Hilbert space. We consider a problem of optimization with the control in coefficients of linear parabolic equation as an example. Using results of Spagnolo we characterize the closure of the reachable set. Finally, we construct an example of an optimization problem with the control in coefficients of a parabolic equation which does not have an optimal solution.

Some problems in determining the lower-order-term coefficients in parabolic equations

Some problems in determining the lower-order-term coefficients in parabolic equations