Inverse problem for elliptic equation in a Banach space with Bitsadze–Samarsky boundary value conditions

Orlovsky, Dmitry

doi:10.1515/jip-2012-0058

Cited by 13 publications

(3 citation statements)

References 6 publications

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“…In recent years, many scientists have greatly increased interest in nonclassical boundary value problems (BVPs) for partial differential equations (PDEs) (see and references therein). In particular, methods of solutions source identification problems (SIPs) for PDEs have been extensively studied by several authors in earlier studies, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]22 and bibliography herein).…”

Section: Introductionmentioning

confidence: 99%

On the stable difference scheme for source identification nonlocal elliptic problem

Ashyralyyev

2022

Math Methods in App Sciences

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Approximation of source identification problem for elliptic equation with integral-type nonlocal condition is discussed. The first order of accuracy difference scheme for elliptic nonlocal identification problem is studied. By using spectral resolution of a self-adjoint operator, we establish stability inequalities for solution of constructed scheme. Subsequently, the difference scheme for approximate solution of multidimensional boundary value problem with integral-type nonlocal and first kind boundary conditions is investigated on stability. Numerical test examples are presented.

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Section: Introductionmentioning

confidence: 99%

On the stable difference scheme for source identification nonlocal elliptic problem

Ashyralyyev

2022

Math Methods in App Sciences

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“…Such problems of retrieving the unknown boundary condition and weights are generally known as inverse problems. Most previous research on these problems has concentrated on approximating parameter estimation [1][2][3][4][5] to some extent. Wei, et al (1998,2003) calculated the weights with the matrix theory and the finite difference method of partial differential equation [6,7].…”

Section: Introductionmentioning

confidence: 99%

Green’s Function for Static Klein–Gordon Equation Stated on a Rectangular Region and Its Application in Meteorology Data Assimilation

Cheng

Jiang

et al. 2021

Atmosphere

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The meteorology data assimilation applications often encounter variational problems with unknown weights, where the corresponding Euler equation is an elliptic partial differential equation. This research focused on retrieving the weights in remote sensing data assimilation by means of the computer-friendly form of the Green’s function obtained by eigenfunction expansion for the boundary value problem of the static Klein–Gordon equation on a rectangular region. With the help of the proposed retrieving method, the assimilation problem of estimating regional precipitation with weather radar and rain-gauge is solved in the Green’s function method. Results show that high accuracy of the proposed method makes it a good candidate for data assimilation problems in operational use.

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“…In papers [29,30], theorem on solvability and uniqueness of solution for problem (2) has been proved. Well-posedness of problem (2) was studied in [16].…”

Section: Introductionmentioning

confidence: 99%

Finite difference method for Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions

Ashyralyyev

Akyuz

2018

Filomat

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In this paper, we apply finite difference method to Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions. Stability, coercive stability inequalities for solution of the first and second order of accuracy difference schemes (ADSs) are proved. Then, established abstract results are applied to get stable difference schemes for Bitsadze-Samarskii type overdetermined elliptic multidimensional differential problems with multipoint nonlocal boundary conditions. Finally, numerical results with explanation on the realization in two dimensional and three dimensional cases are presented.

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Inverse problem for elliptic equation in a Banach space with Bitsadze–Samarsky boundary value conditions

Cited by 13 publications

References 6 publications

On the stable difference scheme for source identification nonlocal elliptic problem

On the stable difference scheme for source identification nonlocal elliptic problem

Green’s Function for Static Klein–Gordon Equation Stated on a Rectangular Region and Its Application in Meteorology Data Assimilation

Finite difference method for Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions

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