Initial‐to‐Interface Maps for the Heat Equation on Composite Domains. Issue 1 (24th June 2016)

• Record Type: Journal Article
• Authors: Sheils, Natalie E.; Deconinck, Bernard
• Other Names: Biondini G. guestEditor.; Fokas A.S. guestEditor.
• Is Part Of: Studies in applied mathematics. Volume 137:Issue 1(2016)
• Page Start: 140
• Page End: 154
• Publication Date: 2016-06-24
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12138
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract : A map from the initial conditions to the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with n interfaces. The existence of this map allows changing the problem at hand from an interface problem to a boundary value problem which allows for an alternative to the approach of finding a closed‐form solution to the interface problem.