Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-09-77-19
DOI: https://dx.doi.org/10.15863/TAS.2019.09.77.19
Language: Russian
Citation: Tursunov, F. R. (2019). Regularization of the Cauchy problem for the first-order linear elliptic systems with constant coefficients in a bounded domain. ISJ Theoretical & Applied Science, 09 (77), 101-106. Soi: http://s-o-i.org/1.1/TAS-09-77-19 Doi: https://dx.doi.org/10.15863/TAS.2019.09.77.19 |
Pages: 101-106
Published: 30.09.2019
Abstract: In the paper the continuation problem for the solution of the first order elliptic type linear system equations with constant coefficients in the domain ?? by given values on the smooth part ?? of the boundary ???? is studied. The considered problem belongs to the problems of mathematical physics, in which there is no continuous dependence of solutions on the initial data. It is assumed that the solution to the problem exists and is continuously differentiable in a closed domain with exactly given Cauchy data. For this case, an explicit formula for the continuation of the solution is established, as well as a regularization formula for the case when, under these conditions, instead of the Cauchy data, their approximations are given with a given error in the uniform metric. We obtain estimates for the stability of the solution of the Cauchy problem in the classical sense.
Key words: Cauchy problem, ill-posed problems, Carleman function, regularized solutions, regularization, continuation formulas.
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