A magneto-viscoelasticity problem with a singular memory kernel. (June 2017)

• Record Type: Journal Article
• Authors: Carillo, Sandra; Chipot, Michel; Valente, Vanda; Vergara Caffarelli, Giorgio
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 200
• Page End: 210
• Publication Date: 2017-06
• Subjects: Magneto-viscoelastic materials -- Nonlinear integro-differential problem -- Materials with memory -- Singular kernel; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.10.014
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The existence of solutions to a one-dimensional problem arising in magneto-viscoelasticity is here considered. Specifically, a non-linear system of integro-differential equations is analysed; it is obtained coupling an integro-differential equation modelling the viscoelastic behaviour, in which the kernel represents the relaxation function, with the non-linear partial differential equations modelling the presence of a magnetic field. The case under investigation generalizes a previous study since the relaxation function is allowed to be unbounded at the origin, provided it belongs to L 1 ; the magnetic model equation adopted, as in the previous results (Carillo et al., 2011, 2012; Chipot et al. 2008, 2009) is the penalized Ginzburg–Landau magnetic evolution equation.