ON A REGULARIZED SOLUTION OF THE CAUCHY PROBLEM FOR MATRIX FACTORIZATIONS OF THE HELMHOLTZ EQUATION

ON A REGULARIZED SOLUTION OF THE CAUCHY PROBLEM FOR MATRIX FACTORIZATIONS OF THE HELMHOLTZ EQUATION

In this paper, we consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a multidimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An approximate solution to this problem is constructed based o...

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Veröffentlicht in:TWMS journal of applied and engineering mathematics 2023-01, Vol.13 (4), p.1311
Hauptverfasser: Juraev, D.A, Noeiaghdam, S, Agarwal, P
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Boundary value problems
Cauchy problems
Differential equations
Fluid dynamics
Helmholtz equations
Matrix methods
Partial differential equations
Physics
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Zusammenfassung:In this paper, we consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a multidimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An approximate solution to this problem is constructed based on the Carleman matrix method. Keywords: Ill-Posed Cauchy Problems, regularized solution, approximate solution, matrix factorization, elliptical system. AMS Subject Classification: 35J46, 35J56
ISSN:2146-1147
2146-1147