Geodesic
Asymptotics of solutions of non-linear dissipative equations
Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 461-492.

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We study the large-time asymptotic behaviour of solutions of the Cauchy problem for a system of non-linear evolution equations with dissipation. In the case when the initial data are small, we construct solutions using the contraction-mapping principle. When the initial data are large, we obtain the large-time asymptotics of solutions by taking into account a certain symmetry of the non-linear terms. 
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E. I. Kaikina; P. I. Naumkin; I. A. Shishmarev. Asymptotics of solutions of non-linear dissipative equations. Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 461-492. http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a3/

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