Existence and Regularity of a Global Attractor for Doubly Nonlinear Parabolic Equations
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In this paper we consider a doubly nonlinear parabolic partial differential equation ∂β(u) / ∂t - Δpu + ƒ(x,t,u) = 0 in Ω x ℝ+, with Dirichlet boundary condition and initial data given. We prove the existence of a global compact attractor by using a dynamical system approach. Under additional conditions on the nonlinearities β, ƒ, and on p, we prove more regularity for the global attractor and obtain stabilization results for the solutions.
CitationEl Hachimi, A., & El Ouardi, H. (2002). Existence and regularity of a global attractor for doubly nonlinear parabolic equations. Electronic Journal of Differential Equations, 2002(45), pp. 1-15.
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