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Vol 230, No 6 (2018)
- Year: 2018
- Articles: 3
- URL: https://journals.rcsi.science/1072-3374/issue/view/14917
Article
On Approximation of Coefficient Inverse Problems for Differential Equations in Functional Spaces
Abstract
This paper is devoted to the theory of approximation of coefficient inverse problems for differential equations of parabolic, elliptic, and hyperbolic types in functional spaces. We present general statements of problems and their approximations and review results obtained earlier in the literature.
823-906
Criteria of the Uniqueness of Solutions and Well-Posedness of Inverse Source Problems
Abstract
In this paper, we study the relation between the well-posedness of the inverse problem of the recovering the source in an abstract differential equation and the basis property of a certain class of function systems in a Hilbert space. As a consequence, based on the results concerning the well-posedness of inverse problems, we obtain the Riesz basis property and—under certain additional conditions—the Bari basis property of such systems.
907-949
Finite-Difference Methods for Fractional Differential Equations of Order 1/2
Abstract
In this work, we study approximations of solutions of fractional differential equations of order 1/2. We present a new method of approximation and obtain the order of convergence. The presentation is given within the abstract framework of a semidiscrete approximation scheme, which includes finite-element methods, finite-difference schemes, and projection methods.
950-960