ON THE CAUCHY PROBLEM FOR MATRIX FACTORIZATIONS OF THE HELMHOLTZ EQUATION

Öz

In the paper it is considered the regularization of the Cauchy problem for systems of elliptic type equations of the first order with constant coefficients factorisable Helmholtz operator in two-dimensional unbounded domain. Using the results of [20, 21, 22, 23, 24, 25 ], we construct in explicit form Carleman matrix and, based on the regularized solution of the Cauchy problem.

Anahtar Kelimeler

• The Cauchy problem,Regularization,Factorization,Regular solution

Kaynakça

1. 1. D.A. Juraev, The Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain, Sib. Electron. Mat. Izv. 14 (2017), 752–764. (in Russian).
2. 2. Cauchy problem for matrix factorizations of the Helmholtz equation, Ukrainian Mathematical Journal. 69 (2018), no. 10., 1583-1592. (Ukrainian Original Vol. 69, No. 10, October, 2017). (in Russian).
3. 3. D.A. Juraev, On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain, Sib. Electron. Mat. Izv. 15 (2018), 11–20. (in Russian).
4. 4. D.A. Juraev, On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain, Journal of Universal Mathematics. 1 (2018), no. 3, 312–319.
5. 5. D.A. Juraev, On the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain in R2, Sib. Electron. Mat. Izv. 15 (2018), 1865–1877. (in Russian).