ABSTRACT: Singularly perturbed evolution equations may be analyzed by various techniques. In this paper, we focus on ideas of asymptotic
analysis and those akin to the Trotter–Kato approximation theorems. Using as an example an abstract telegraph-type system,
we show how these two approaches intertwine and complement each other. The paper also may be seen as a continuation of Kato’s
project (in Turbululence and Navier–Stokes Equations Theory. Proc. Conf. Univ. Paris-Sud, Orsay 1975, Lect. Notes Math., Springer,
Berlin, vol 565, pp. 104–112, 1976) taking account of recent results.
Journal of Evolution Equations 04/2012; 9(2):293-314. · 0.88 Impact Factor