Abstract
In this paper, we consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a three-dimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An approximate solution to this problem is constructed based on the Carleman matrix method.
Publisher
Sociedade Paranaense de Matematica
Reference46 articles.
1. A.N. Tikhonov, On the solution of ill-posed problems and the method of regularization, Reports of the USSR Academy of Sciences, 151(3), 501-504, (1963).
2. A. Shokri, M.M. Khalsaraei, S. Noeiaghdam, D.A. Juraev, A new divided difference interpolation method for twovariable functions, Global and Stochastic Analysis, 9(2), 1-8, (2022).
3. A.T. Ramazanova, On determining initial conditions of equations flexural-torsional vibrations of a bar, European Journal of Pure and Applied Mathematics, 12(1), 25-38, (2019). https://doi.org/10.29020/nybg.ejpam.v12i1.3350
4. A.T. Ramazanova, Necessary conditions for the existence of a saddle point in one optimal control problem for systems of hyperbolic equations, European Journal of Pure and Applied Mathematics, 14(4), 1402-1414, (2021). https://doi.org/10.29020/nybg.ejpam.v14i4.4135
5. B.C. Corcino, R.B. Corcino RB, B.A.A. Damgo, J.A.A. Ca˜nete, Integral representation and explicit formula at rational arguments for Apostol - Tangent polynomials, Symmetry, 14(1), 1-10, (2022). https://doi.org/10.3390/sym14010053