Asymptotic estimates in Thompson's metric for semilinear parabolic equations. (January 2016)

• Record Type: Journal Article
• Authors: Herzog, Gerd; Kunstmann, Peer Chr.
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 112
• Page End: 120
• Publication Date: 2016-01
• Subjects: 47J35 -- 47B60 -- 47H09 -- 35K55; Semilinear parabolic equations -- Asymptotic stability -- Thompson metric; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.09.027
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In ordered Banach spaces we prove exponential asymptotic stability estimates in Thompson's metric for the semilinear equation u ′ = A u + f ( u ), where A is the generator of a positive and exponentially stable C 0 -semigroup and f is a contraction with respect to Thompson's metric. We apply our results to the study of the semilinear parabolic equation u ′ ( t ) = Δ u ( t ) + u ( t ) κ with homogeneous Dirichlet boundary conditions on bounded domains where ∣ κ ∣ < 1 .