Linear chaos and approximation
This work deals with the chaoticity of semigroups. Let \((T_n(t))_{t\geq 0}\) be a sequence of strongly continuous linear semigroups on Banach spaces \(X_n\) converging in the sense of Kato to a semigroup \((T(t))_{t\geq 0}\) on the Banach space \(X\). Under some assumptions, the authors show that the chaoticity of the family of the semigroup \((T_n(t))_{t\geq 0}\) is inherited by the semigroup \((T(t))_{t\geq 0}\). Some applications on the discrete parabolic equation are given at the end of this work.
scientific article; zbMATH DE number 1495769
scientific article