On Long-Time Dynamics of the Solution of Doubly Nonlinear Equation

• Published in: Qualitative theory of dynamical systems Vol. 15; no. 1; pp. 127 - 155
• Main Authors: Novruzov, Emil, Hagverdiyev, Ali
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2016
• Subjects: Difference and Functional Equations; Dynamical Systems and Ergodic Theory; Mathematics; Mathematics and Statistics; 35B41; Nonlinear degenerate equation; Finite speed of propagation of perturbations (FSP); 35B45; 35K55; Global attractor
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-015-0153-0

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.