Geodesic
The Singular Limit of the Dissipative Zakharov System
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 75-99 
A. S. Shcherbina. The Singular Limit of the Dissipative Zakharov System. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 75-99. http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The dissipative Zakharov system which models the propagation of Langmuir waves in plasmas is considered on the interval $[0,L]$. We are interested in the case of large ion acoustic speed $\lambda$. After the formal limiting transition $\lambda\to\infty$ this system turns into the coupling system of the parabolic and Schrödinger equations. We prove that this limit system has a solution and generates a dissipative dynamical system possessing a global compact attractor. Our main result is the upper semicontinuity of the attractor as $\lambda\to\infty$.

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