Regularization of the Ill-Posed Cauchy Problem for Matrix Factorizations of the Helmholtz Equation on the Plane

In this paper, we present an explicit formula for the approximate solution of the Cauchy problem for the matrix factorizations of the Helmholtz equation in a bounded domain on the plane. Our formula for an approximate solution also includes the construction of a family of fundamental solutions for t...

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Bibliographic Details
Published in:Axioms 2021, Vol.10 (2), p.82
Main Authors: Juraev, Davron Aslonqulovich, Noeiaghdam, Samad
Format: Article
Language:English
Subjects:
Boundary value problems
cauchy problem
Cauchy problems
factorization
Formulas (mathematics)
fundamental solution
Helmholtz equations
Operators (mathematics)
Partial differential equations
regular solution
Regularization
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Summary:In this paper, we present an explicit formula for the approximate solution of the Cauchy problem for the matrix factorizations of the Helmholtz equation in a bounded domain on the plane. Our formula for an approximate solution also includes the construction of a family of fundamental solutions for the Helmholtz operator on the plane. This family is parameterized by function K(w) which depends on the space dimension. In this paper, based on the results of previous works, the better results can be obtained by choosing the function K(w).
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10020082