Year: 2025
Type: article
Abstract: We investigate Trotter–Kato approximation results for the class of bi-continuous cosine families. After a concise overview of bi-continuous cosine families, we introduce uniformly bi-continuous cosine families and prove, under natural resolvent-convergence assumptions, a Trotter–Kato approximation theorem. This result both generalizes and refines existing approximation theorems for strongly continuous cosine families. To illustrate the power of our approach, we construct an explicit mollification procedure on Cb(R), yielding a practical approximation of solutions of the wave equation. The techniques developed here open new directions for rigorous numerical analysis of evolution equations that lack strong continuity and provide a framework functional analytic approaches tp partial differential equations.
Source: Contemporary Mathematics
Author: Christian Budde
Institution: University of the Free State
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
Funder: National Research Foundation
Award: G2042216116
OpenAlex ID: W4414623392
FWCI:
Cites:
Cited by:
Related to: