Global attractors for doubly nonlinear evolution equations with non-monotone perturbations

2008/10/01 by Goro Akagi, Akagi, Goro
Computer Science · Engineering · Mathematics · #34G25 #35B41 #35K65 #37L30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations #math.AP #math.DS #msc:34G25 #msc:35B41 #msc:35K65 #msc:37L30

paper · pdf · doi:10.48550/arxiv.0810.0191

openalex publication_date 2008/10/01 · arxiv created 2010/07/30 · arxiv updated 2010/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper proposes an abstract theory concerned with dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to construct global attractors, an approach based on the notion of generalized semiflow is employed instead of the usual semi-group approach, since solutions of the Cauchy problem for the equation might not be unique. Moreover, the preceding abstract theory is applied to a generalized Allen-Cahn equation whose potential is divided into a convex part and a non-convex part as well as a semilinear parabolic equation with a nonlinear term involving gradients.

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