Geodesic
On the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain in ${\mathbb R}^{2}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1865-1877

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In the paper it is considered the problem of regularization of the Cauchy problem for matrix factorisations of the Helmholtz equation in an unbounded planar domain. Using the Carleman matrix found an explicitly regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in two-dimensional unbounded domain.
Keywords: the Cauchy problem, regularization, factorization, regular solution, fundamental solution. 
@article{SEMR_2018_15_a147,
     author = {D. A. Juraev},
     title = {On the {Cauchy} problem for matrix factorizations of the {Helmholtz} equation in an unbounded domain in ${\mathbb R}^{2}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1865--1877},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a147/}
}
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D. A. Juraev. On the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain in ${\mathbb R}^{2}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1865-1877. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a147/