Abstract
We study the Dirichlet mixed problem for a class of parabolic equation with double non-power nonlinearities in cylindrical domain �� = (t > 0) × Ω. By the Galerkin approximations method suggested by Mukminov F.Kh. for a parabolic equation with dou- ble nonlinearities we prove the existence of strong solutions in Sobolev-Orlicz space. The maximum principle as well as upper and lower estimates characterizing powerlike decay of solution as t → ∞ in bounded and unbounded domains Ω ⊂ R n are established.
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