Geodesic
Solvability of a~mixed problem for the nonlinear Schr\"odinger equation
Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 525-540

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

Existence and uniqueness theorems are established for a generalized solution of a mixed problem for the nonlinear Schrödinger equation in the presence of dissipation in the space $L_\infty(0,T;\overset\circ W{}^1_2(G))$ and $L_\infty(0,T;\overset\circ W{}^1_2(G)\cap W^2_2(G))$. The method of proving uniqueness of a solution is based on the assumption of the existence and boundedness in $t\in[0,T]$ of the integral of a solution $\int_G\exp(\varkappa|u|^p)\,dx$ for some $\varkappa>0$, where $p$ is the degree of nonlinearity in the equation. Bibliography: 16 titles. 
@article{SM_1987_58_2_a13,
     author = {M. V. Vladimirov},
     title = {Solvability of a~mixed problem for the nonlinear {Schr\"odinger} equation},
     journal = {Sbornik. Mathematics},
     pages = {525--540},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_58_2_a13/}
}
TY  - JOUR
AU  - M. V. Vladimirov
TI  - Solvability of a~mixed problem for the nonlinear Schr\"odinger equation
JO  - Sbornik. Mathematics
PY  - 1987
SP  - 525
EP  - 540
VL  - 58
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1987_58_2_a13/
LA  - en
ID  - SM_1987_58_2_a13
ER  - 
%0 Journal Article
%A M. V. Vladimirov
%T Solvability of a~mixed problem for the nonlinear Schr\"odinger equation
%J Sbornik. Mathematics
%D 1987
%P 525-540
%V 58
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1987_58_2_a13/
%G en
%F SM_1987_58_2_a13
M. V. Vladimirov. Solvability of a~mixed problem for the nonlinear Schr\"odinger equation. Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 525-540. http://geodesic.mathdoc.fr/item/SM_1987_58_2_a13/