Global asymptotic stability for semilinear equations via Thompson's metric

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Global asymptotic stability for semilinear equations via Thompson's metric

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Title: Global asymptotic stability for semilinear equations via Thompson's metric
Author: Herzog, G.; Kunstmann, P.C.
Abstract: In ordered Banach spaces we prove the global asymptotic stability of the unique strictly positive equilibrium of the semilinear equation u′ = Au + ꭍ(u), if A is the generator of a positive and exponentially stable C₀-semigroup and ꭍ is a contraction with respect to Thompson's metric. The given estimates show that convergence holds with a uniform exponential rate.
URI: http://hdl.handle.net/10662/10151
Date: 2014


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