Geodesic
Solvability of a mixed problem for the nonlinear Schrödinger equation
Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 525-540 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {M. V. Vladimirov},
     title = {Solvability of a~mixed problem for the nonlinear {Schr\"odinger} equation},
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M. V. Vladimirov. Solvability of a mixed problem for the nonlinear Schrödinger equation. Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 525-540. http://geodesic.mathdoc.fr/item/SM_1987_58_2_a13/

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