Geodesic
On the Cauchy problem for the biharmonic equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 201-215

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: biharmonic equations, Cauchy problem, ill-posed problems, Carleman function, regularized solutions, regularization, continuation formulas. 
@article{JSFU_2022_15_2_a6,
     author = {Dilshod S. Shodiev},
     title = {On the {Cauchy} problem for the biharmonic equation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {201--215},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a6/}
}
TY  - JOUR
AU  - Dilshod S. Shodiev
TI  - On the Cauchy problem for the biharmonic equation
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 201
EP  - 215
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a6/
LA  - en
ID  - JSFU_2022_15_2_a6
ER  - 
%0 Journal Article
%A Dilshod S. Shodiev
%T On the Cauchy problem for the biharmonic equation
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 201-215
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a6/
%G en
%F JSFU_2022_15_2_a6
Dilshod S. Shodiev. On the Cauchy problem for the biharmonic equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 201-215. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a6/