Lower semicontinuity of global attractors for a class of evolution equations type neural fields in a bounded domain

الأصل · EN

In this work we consider the nonlocal evolution equation ∂ 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 L²(S¹), where S¹ denotes the unit sphere. We obtain stronger results on existence of global attractors and Lypaunov functional than the already existing in the literature. Furthermore, we prove the result, not yet known in the literature, of lower semicontinuity of global attractors with respect to connectivity function J.