Geodesic
On uniqueness classes of solutions of the first mixed problem for a~quasi-linear second-order parabolic system in an unbounded domain
Izvestiya. Mathematics , Tome 65 (2001) no. 3, pp. 469-484.

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We study a quasi-linear parabolic system of divergence type having an energy inequality and satisfying monotonicity conditions. For such a system, the first mixed problem is considered in a cylindrical domain $\{t>0\}\times\Omega$ that is unbounded with respect to the spatial variables. Generally, the initial vector function $\varphi$ in the problem may not belong to $\mathbb L_2(\Omega)$. A uniqueness class close to that of Täcklind [3] is established for the solutions of this problem. Moreover, a uniqueness theorem is proved for a solution belonging to this class and having an initial vector function increasing at infinity. 
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L. M. Kozhevnikova. On uniqueness classes of solutions of the first mixed problem for a~quasi-linear second-order parabolic system in an unbounded domain. Izvestiya. Mathematics , Tome 65 (2001) no. 3, pp. 469-484. http://geodesic.mathdoc.fr/item/IM2_2001_65_3_a2/

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