2013/02/18 by Ciprian G. Gal, Gal, Ciprian G., Joseph L. Shomberg +1
Computer Science · Engineering · Mathematics · #35B21 #35K57 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Primary: 35B41 #Secondary: 35L20 #Stability and Controllability of Differential Equations #math.AP #math.DS #msc:35B21 #msc:35B41 #msc:35K57 #msc:35L20
paper · pdf · doi:10.48550/arxiv.1302.4265
to appear in Quarterly of Applied Mathematics
openalex publication_date 2013/02/18 · arxiv created 2013/04/18 · arxiv updated 2013/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.