Article

    Ufa Mathematical Journal
    Volume 6, Number 2, pp. 3-24

    Estimates of decay rate for solution to parabolic equation with non-power nonlinearities


    Andriyanova E.R.

    DOI:10.13108/2014-6-2-3

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    We study the Dirichlet mixed problem for a class of parabolic equation with double non-power nonlinearities in cylindrical domain $D=(t>0)\times\Omega$. By the Galerkin approximations method suggested by Mukminov F.Kh. for a parabolic equation with double 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 $t\to \infty$ in bounded and unbounded domains $\Omega\subset \mathds{R}^n$ are established.