Geodesic
Existence and qualitative properties of~a~solution of~the~first mixed problem for a~parabolic~equation with non-power-law double nonlinearity
Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 1-40

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The first mixed problem is investigated for a certain class of parabolic equations with double non-power-law nonlinearities in a cylindrical domain of the form $D=(t>0)\times\Omega$. The domain $\Omega\subset \mathbb R^n$ can be unbounded. The existence of strong solutions in a Sobolev-Orlicz space is proved by the method of Galerkin approximations. A maximum principle is established, and upper and lower bounds characterizing the power-law decay of solution as $t\to \infty$ are proved. The uniqueness of the solution is proved under certain additional assumptions. Bibliography: 29 titles.
Keywords: parabolic equation with double nonlinearity, $N$-functions, estimate for the decay rate of a solution.
Mots-clés : existence of a solution 
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È. R. Andriyanova; F. Kh. Mukminov. Existence and qualitative properties of~a~solution of~the~first mixed problem for a~parabolic~equation with non-power-law double nonlinearity. Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 1-40. http://geodesic.mathdoc.fr/item/SM_2016_207_1_a0/