On the Cauchy problem for the biharmonic equation

Dilshod S. Shodiev

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 201-215.

Résumé

The work is devoted to the study of continuation and stability estimation of the solution of the Cauchy problem for the biharmonic equation in the domain $G$ from its known values on the smooth part of the boundary $\partial G$. The problem under consideration belongs to the problems of mathematical physics in which there is no continuous dependence of solutions on the initial data. In this work, using the Carleman function, not only the biharmonic function itself, but also its derivatives are restored from the Cauchy data on a part of the boundary of the region. The stability estimates for the solution of the Cauchy problem in the classical sense are obtained.

Détail

Keywords: biharmonic equations, Cauchy problem, ill-posed problems, Carleman function, regularized solutions, regularization, continuation formulas.

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