Estimates of decay rate for solution to parabolic equation with non-power nonlinearities
Elina Radikovna Andriyanova · Ufimskii Matematicheskii Zhurnal · 2014
We study the Dirichlet mixed problem for a class of parabolic equation with double non-power nonlinearities in cylindrical domain 𝐷 = (𝑡 > 0) × Ω.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 → ∞ in bounded and unbounded domains Ω ⊂ R 𝑛 are established.