A magneto-viscoelasticity problem with a singular memory kernel

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• 作者：Sandra Carillo^a ; ^b ; ^{sandra.carillo@sbai.uniroma1.it} ; ^{sandra.carillo@uniroma1.it} ; Michel Chipot^c ; Vanda Valente^d ; Giorgio Vergara Caffarelli^a
• 关键词：Magneto-viscoelastic materials ; Nonlinear integro-differential problem ; Materials with memory ; Singular kernel
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：200-210
• 全文大小：593 K
• 卷排序：35

文摘

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 L1L1; 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.