On some identification problem for source function to one semievolutionary system
-
Yuri Y. Belov
and
Vera G. Kopylova
Abstract.
We solve an identification problem for source functions to one-dimensional second order parabolic-elliptic system. Considered the system of equations obtained from the original system, where the time derivative added to the elliptic equation, containing a small parameter 
, we prove the following: the solvability “in general” of the inverse problem for , uniqueness of classical solutions of the inverse problem, periodicity of the spatial variable solutions of approximating problems for , a priori (uniform in ) estimates of solutions of approximating problems, convergence on the basis of the a priori estimates of solutions approximating the inverse problems to solutions original for 
, the rate of convergence (order 
) of solutions of approximating problems in classes of continuous functions. An identification problem of source functions in the system of composite type is treated by some authors. The case where the unknown component of the vector source function in the equation that does not contain the small parameter was studied by Belov (2010).
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Extra-optimal methods for solving ill-posed problems
- Regularization for ill-posed parabolic evolution problems
- Satisfier function in Ritz–Galerkin method for the identification of a time-dependent diffusivity
- On some identification problem for source function to one semievolutionary system
- Regularization of backward parabolic equations in Banach spaces
- On the existence of global saturation for spectral regularization methods with optimal qualification
- Inverse determination of unsteady temperatures and heat fluxes on inaccessible boundaries
- Well-posedness of the Cauchy problem to a nonlinear magnetoelastic system in 1-D periodic media
- A family of rules for the choice of the regularization parameter in the Lavrentiev method in the case of rough estimate of the noise level of the data
- Inverse problems for second-order differential pencils with Dirichlet boundary conditions
