Existence and uniqueness of the modified error function. (August 2017)

• Record Type: Journal Article
• Authors: Ceretani, Andrea N.; Salva, Natalia N.; Tarzia, Domingo A.
• Is Part Of: Applied mathematics letters. Volume 70(2017:Aug.)
• Page Start: 14
• Page End: 17
• Publication Date: 2017-08
• Subjects: Modified error function -- Error function -- Phase change problem -- Temperature-dependent thermal conductivity -- Nonlinear second order ordinary differential equation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2017.02.017
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This article is devoted to the proof of the existence and uniqueness of the modified error function introduced in Cho and Sunderland (1974). This function is defined as the solution to a nonlinear second order differential problem depending on a real parameter. We prove here that this problem has a unique non-negative analytic solution when the parameter assumes small positive values.