Geodesic
A problem with nonlocal conditions for a one-dimensional parabolic equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 380-395

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

In present paper, we consider a problem with nonlocal conditions for parabolic equation and show that there exists a unique weak solution in Sobolev space. The main tool to prove the existence of a unique weak solution to the problem is a priori estimates derived by authors. We also note a connection between Steklov nonlocal conditions and first kind integral conditions. This connection enables interpret the problem under consideration as a problem with perturbed Steklov nonlocal conditions. Obtained results may be useful for certain class of problems including inverse problems.
Mots-clés : parabolic equation, nonlocal conditions
Keywords: boundary-value problem, generalized solution; Sobolev spaces. 
@article{VSGTU_2022_26_2_a10,
     author = {A. B. Beylin and A. V. Bogatov and L. S. Pulkina},
     title = {A problem with nonlocal conditions for a one-dimensional parabolic equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {380--395},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a10/}
}
TY  - JOUR
AU  - A. B. Beylin
AU  - A. V. Bogatov
AU  - L. S. Pulkina
TI  - A problem with nonlocal conditions for a one-dimensional parabolic equation
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2022
SP  - 380
EP  - 395
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a10/
LA  - ru
ID  - VSGTU_2022_26_2_a10
ER  - 
%0 Journal Article
%A A. B. Beylin
%A A. V. Bogatov
%A L. S. Pulkina
%T A problem with nonlocal conditions for a one-dimensional parabolic equation
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2022
%P 380-395
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a10/
%G ru
%F VSGTU_2022_26_2_a10
A. B. Beylin; A. V. Bogatov; L. S. Pulkina. A problem with nonlocal conditions for a one-dimensional parabolic equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 380-395. http://geodesic.mathdoc.fr/item/VSGTU_2022_26_2_a10/