On Long-Time Dynamics of the Solution of Doubly Nonlinear Equation - Novruzov, Emil; Hagverdiyev, Ali (Qualitative theory of dynamical systems, 2016)
The subject of this investigation is the long time behavior of the positive solutions of the following nonhomogeneous equation 1 ρ x ∂ β v ∂ t - ∑ i = 1 N D i ( | D i v | λ - 1 D i v ) + ρ x g β v + l β 1 + m v = f x in unbounded domain R + × R N , where the term g s is supposed to satisfy a condition g ′ s > - l 1 and D i = ∂ x i . The existence of the global attractor for the Eq. ( 1 ) in L 1 + θ R N , ρ = v ; v ρ 1 / ( 1 + θ ) ∈ L 1 + θ R N is proved.