On the Approximate Solution of the Cauchy Problem in a Multidimensional Unbounded Domain

Abstract

In this paper, the Carleman matrix is constructed, and based on it we found explicitly a regularized solution of the Cauchy problem for the matrix factorization of the Helmholtz equation in a multidimensional unbounded domain in Rm,(m=2k,k≥2). The corresponding theorems on the stability of the solution of problems are proved.

Keywords

• integral formula
• regularization of the Cauchy problem
• approximate solution
• Carleman matrix
• family of vector functions
• Bessel and Hankel functions