A series of （Sm, Tb）FeCo/Cr/TbFeCo trilayers with perpendicular anisotropy was prepared by RF magnetron sputtering, and the effect of Cr interlayer thickness on magnetic properties and interlayer exchange coupling was investigated. All the samples showed strong out-of-plane anisotropy but their hysteresis loops displayed two types ： singlephase and double-phase, indicating that interlayer exchange coupling and magnetic properties varied with the thickness of Cr interlayer. Both saturation field Hs and （1-Mr/Ms） curves indicated that interlayer exchange coupling oscillated between antiferromagnetic and ferromagnetic with a period of 1.6 nm, and the oscillation strength attenuated with increasing Cr interlayer thickness. After being annealed at 450℃ for 25 min, the hysteresis loops of all the samples became single-phase type and coercivity Hc decreased greatly, which could be attributed to the decrease of effective anisotropy in （Sm, TbFeCo） grains.
In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a nonlinear parabolic partial differential equation, which is related to the Malik-Perona model in image analysis.
