Geodesic
On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 11-20

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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 three-dimensional bounded 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_2018_15_a84,
     author = {D. A. Juraev},
     title = {On the {Cauchy} problem for matrix factorizations of the {Helmholtz} equation in a bounded domain},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {11--20},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a84/}
}
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D. A. Juraev. On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 11-20. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a84/