Lower Semicontinuity of Global Attractors for a Class of Evolution Equations of Neural Fields Type in a Bounded Domain
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DOI: 10.1007/s12591-015-0258-6
Abstract: In this work we consider the nonlocal evolution equation $$\displaystyle \frac{\partial u(w,t)}{\partial t}=-u(w,t)+ \int _{S^{1}}J(wz^{-1})f(u(z,t))\mathrm{d}z+ h, \quad h > 0,$$∂u(w,t)∂t=-u(w,t)+∫S1J(wz-1)f(u(z,t))dz+h,h>0,which arises in models of neuronal activity, in $$L^{2}(S^{1})$$L2(S1), where $$S^{1}$$S1 denotes the unit sphere. We… read more here.
Keywords: evolution; global attractors; semicontinuity global; attractors class ... See more keywords