Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity. (11th March 2016) - Andriyanova, È R; Mukminov, F Kh
Abstract: 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)×Ω$ . The domain$ Ω\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→ ∞$ are proved. The uniqueness of the solution is proved under certain additional assumptions. Bibliography: 29 titles.