ON A REGULARIZED SOLUTION OF THE CAUCHY PROBLEM FOR MATRIX FACTORIZATIONS OF THE HELMHOLTZ EQUATION

ON A REGULARIZED SOLUTION OF THE CAUCHY PROBLEM FOR MATRIX FACTORIZATIONS OF THE HELMHOLTZ EQUATION

D. A. Juraev, S. Noeiaghdam, P. Agarwal

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Abstract

In this paper, we consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a multidimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An ap- proximate solution to this problem is constructed based on the Carleman matrix method.

Keywords

Ill-Posed Cauchy Problems, regularized solution, approximate solution, ma- trix factorization, elliptical system.