ON THE CAUCHY PROBLEM FOR MATRIX FACTORIZATIONS OF THE HELMHOLTZ EQUATION

Yıl 2019, Cilt: 2 Sayı: 2, 113 - 126, 29.07.2019

Davron Juraev

https://doi.org/10.33773/jum.543320

Cited By: 4

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. 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. 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. 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. 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. 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).