The existence of solutions to a one-dimensional problem arising in magneto- viscoelasticity is here considered. Specifically, a non-linear system of integro- dierential equations is analysed; it is obtained coupling an integro-dierential equation modelling the viscoelastic behaviour, in which the kernel represents the relaxation function, with the non-linear partial dierential 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 L1; 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.
A magneto-viscoelasticity problem with a singular memory kernel / Carillo, Sandra; Chipot, M; Valente, V; Vergara Caffarelli, G.. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - STAMPA. - 35:C(2017), pp. 200-210. [10.1016/j.nonrwa.2016.10.014]
A magneto-viscoelasticity problem with a singular memory kernel
CARILLO, Sandra
Primo
;
2017
Abstract
The existence of solutions to a one-dimensional problem arising in magneto- viscoelasticity is here considered. Specifically, a non-linear system of integro- dierential equations is analysed; it is obtained coupling an integro-dierential equation modelling the viscoelastic behaviour, in which the kernel represents the relaxation function, with the non-linear partial dierential 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 L1; 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.File | Dimensione | Formato | |
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