Abstract
In ordered Banach spaces we prove exponential asymptotic stability estimates in Thompson’s metric for the semilinear equation u′=Au+f(u), where A is the generator of a positive and exponentially stable C0-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)=Δu(t)+u(t)κ with homogeneous Dirichlet boundary conditions on bounded domains where ∣κ∣<1.
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