AC0-semigroupS(t),t≥0, on a Banach spaceX(weakly, strongly, uniformly) approachesbalanced (or asynchronous) exponential growthif there exists somes∈R such that[formula]exists (in the weak, strong, uniform operator topology) andPis not the 0 operator. In this paper, the strong and uniform approach to balanced exponential growth is characterized and applicable sufficient conditions are derived. The results will be applied to models for age-size-structured population dynamics in a forthcoming publication.
- Semigroups; dual semigroups; essentially norm-continuous semigroups; Cauchy problems; positive perturbations; balanced (asynchronous) exponential growth
ASJC Scopus subject areas
- Applied Mathematics