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Ellahiani, Idriss; Essoufi, El-Hassan; Tilioua, Mouhcine

Global existence of weak solutions to a three-dimensional fractional model in magneto-viscoelastic interactions. (English) Zbl 1483.74032

Bound. Value Probl. 2017, Paper No. 122, 20 p. (2017).
Summary: In this paper, we prove the existence of global weak solutions for a model described by the fractional Heisenberg equation for the magnetization field and the viscoelastic integro-differential equation for the displacements. We study the three-dimensional case. The demonstration of the existence of weak solution is based on the method of Faedo-Galerkin; and to get the convergence of the nonlinear terms, we introduce the commutator structure.

Cited in 2 Documents

MSC:

74G22 Existence of solutions of equilibrium problems in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory
74F15 Electromagnetic effects in solid mechanics
35D30 Weak solutions to PDEs
35R11 Fractional partial differential equations

Keywords:

three-dimensional periodical fractional Heisenberg equation; equation of viscoelasticity; weak solution; commutator estimates
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References:

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