Convergence theorems for integrated semigroups
Stavros N Busenberg, Binghui Wu · Differential and Integral Equations · 1992
Theorems giving the continuous dependence of an integrated scrnigroup on its infinitesimal generator arc proved.These results generalize the Trotter and Trotter-Kato theorems for C0 sernigroups.They are useful in the study of the convergence of numerical approximations of certain hyperbolic initial value problems which can be formulated as abstract Cauchy problems and which naturally lead to integrated semigroups.The relation of these results with the corresponding classical sernigroup theorems are discussed.