Geodesic
The Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 752-764

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In the paper it is considered the problem of regularization of the Cauchy problem for systems of elliptic type equations of the first order with constant coefficients factorisable Helmholtz operator in threedimensional unbounded domain. Using the results of [1-6], is constructed explicitly Carleman matrix and, based on the regularized solution of the Cauchy problem.
Keywords: the Cauchy problem, regularization, factorization, regular solution, fundamental solution. 
@article{SEMR_2017_14_a119,
     author = {D. A. Juraev},
     title = {The {Cauchy} problem for matrix factorizations of the {Helmholtz} equation in an unbounded domain},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {752--764},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a119/}
}
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D. A. Juraev. The Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 752-764. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a119/