On operator norm convergence in time‐dependent homogenisation problems. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Waurick, Marcus
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800009
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Using the d ‐dimensional wave equation as a prime example, we shall show that an elementary functional analytic theorem for compact operators leads to operator norm convergence of the solution operators of the homogenisation for the wave equation considered as operators in space‐time. The results imply convergence of the amplitude functions locally in L 2 with respect to the temporal and globally in L 2 with respect to the spatial variables.