Geodesic
Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 129-140

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

We discuss questions on the unique solvability of inverse boundary-value source problems for a certain nonlinear integro-differential equation of Boussinesq type with degenerate kernel. We develop the method of degenerate kernels for the inverse boundary-value problem for a fourth-order integro-differential partial differential equation. Using the Banach fixed-point theorem, we prove the uniquely solvability of the problem and establish a criterion of stability of solutions with respect to recovery functions.
Keywords: inverse boundary-value problem, integro-differential Boussinesq-type equation, degenerate kernel, unique solvability. 
@article{INTO_2018_149_a14,
     author = {T. K. Yuldashev},
     title = {Inverse {Boundary-Value} {Problem} for an {Integro-Differential} {Boussinesq-type} {Equation} with {Degenerate} {Kernel}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {129--140},
     publisher = {mathdoc},
     volume = {149},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_149_a14/}
}
TY  - JOUR
AU  - T. K. Yuldashev
TI  - Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 129
EP  - 140
VL  - 149
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_149_a14/
LA  - ru
ID  - INTO_2018_149_a14
ER  - 
%0 Journal Article
%A T. K. Yuldashev
%T Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 129-140
%V 149
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_149_a14/
%G ru
%F INTO_2018_149_a14
T. K. Yuldashev. Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 129-140. http://geodesic.mathdoc.fr/item/INTO_2018_149_a14/