Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity

È. R. Andriyanova   ; F. Kh. Mukminov

Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 1-40

Résumé

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.

Détail

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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