|
Boundary problems for Helmholtz equation and the Cauchy problem for Dirac operators
Alexander A. Shlapunov Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
Abstract:
Studying an operator equation $Au=f$ in Hilbert spaces one usually needs the adjoint operator $A^\star$ for $A$. Solving the ill-posed Cauchy problem for Dirac type systems in the Lebesgue spaces by an iteration method we propose to construct the corresponding adjoint operator with the use of normally solvable mixed problem for Helmholtz Equation. This leads to the description of necessary and sufficient solvability conditions for the Cauchy Problem and formulae for its exact and approximate solutions.
Keywords:
mixed problems, Helmholtz equation, Dirac operators, ill-posed Cauchy problem.
Full text:
PDF file (219 kB)
References:
PDF file
HTML file
UDC:
517.955+517.55 Received: 01.12.2010 Received in revised form: 01.12.2010 Accepted: 15.01.2011
Language:
Citation:
Alexander A. Shlapunov, “Boundary problems for Helmholtz equation and the Cauchy problem for Dirac operators”, J. Sib. Fed. Univ. Math. Phys., 4:2 (2011), 217–228
Citation in format AMSBIB
\Bibitem{Shl11}
\by Alexander~A.~Shlapunov
\paper Boundary problems for Helmholtz equation and the Cauchy problem for Dirac operators
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 2
\pages 217--228
\mathnet{http://mi.mathnet.ru/jsfu180}
\elib{https://elibrary.ru/item.asp?id=15607703}
Linking options:
http://mi.mathnet.ru/eng/jsfu180 http://mi.mathnet.ru/eng/jsfu/v4/i2/p217
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
|
Number of views: |
This page: | 256 | Full text: | 83 | References: | 22 |
|