Solutions to higher-order anisotropic parabolic equations in unbounded domains

Existence of solution for parabolic equation with non-power nonlinearities

“…i.e., ( ) satisfies ∆ 2 -condition. By (5) it yields (18). We observe that if → in (Ω) and satisfies ∆ 2 -condition, then there exists such that ⟨ ( )⟩ .…”

“…In order to prove that ′ ∈ 2 ( ), we apply condition (18): ( , )) ′ , (44) is proven and ′ ( , ) ′ ∈ 1 ( ). We let (ℎ) = (ℎ,∞) .…”

“…There were also obtained exact two-sided estimates for the power decay of norm of solution in time. In [18] there was also considered the case of anisotropic parabolic equations.…”

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

“…∈ Ω as ∈ R. The existence and uniqueness of the solutions to nonlinear parabolic equations were considered in works [1]- [4], [7], [19]- [25] and others. The problem were mainly considered for a bounded domain Ω and on a bounded time interval [0, ] for an arbitrary > 0.…”

“…Work [6] was devoted to the study of the behavior as → ∞ of solution to a mixed problem for an isotropic parabolic equations with a double nonlinearity, while for anisotropic equations with a double nonlinearity the same was done in works [7]- [9]. In work [10] there was studied the degeneration property for the solution to a nonlinear parabolic equation with a non-standard anisotropic growth conditions in a finite time interval.…”