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We establish the existence of infinitely many weak solutions for the general one-dimensional forward–backward diffusion equation ut=σ(ux)x under the homogeneous Neumann boundary condition by rephrasing it as a first-order differential inclusion problem.

Addition of nonsuperconducting phases, such as carbon nanotubes, can modify the superconducting properties of MgB 2 samples, improving the critical current density and upper critical field. A full understanding of the flux creep mechanism involved is crucial to the development of superconducting magnets in persistent mode, one of the main thrusts for the development of MgB 2 wires. In this paper we present a creep study in bulk MgB 2 samples, pure and with different amounts of carbon nanotubes additions. We conclude that the most consistent picture at low temperatures is a single vortex pinning regime, where the correlation length is limited by the grain size. We introduce a novel analysis that allows us to identify the region where the Anderson-Kim model is valid. © 2013 AIP Publishing LLC. Fil:Pasquini, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Serquis, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Civale, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

A control system described by fractional evolution integro-differential equations and fractional integral nonlocal control conditions is investigated. This posed system is subjected to mixed multivalued control constraints whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraints on the controls are the closed convex hulls of the original constraints. More precisely, existence results for the mentioned nonlocal control systems are proved. Furthermore, we study relations between the solution sets of both two systems.