Estimation of the rate of convergence of semigroups to an asynchronous equilibrium. (English) Zbl 0972.47028
Denote \(T(t)\) the semigroup of linear operators defined on some Banach space \(B\). Asynchronous exponential growth occurs when one can determine a pair \((\lambda_0,v)\), \(\lambda_0\in{\mathbb{R}}\), \(0\neq v\in B\), such that \(e^{-\lambda_0 t}T(t)x - c v\to 0\) as \(t\to +\infty\) for every \(x\in B\) and some \(c\in{\mathbb{R}}\). The main result of the paper is an estimate of the rate of convergence of \(T(t)\) to an asynchronous equilibrium. The particular case of translation semigroups is examined.
The results obtained are applied to an equation in demography.
The results obtained are applied to an equation in demography.
Reviewer: Michael Perelmuter (Kyïv)
MSC:
47D06 | One-parameter semigroups and linear evolution equations |
92D25 | Population dynamics (general) |