Lower Semicontinuity of Global Attractors for a Class of Evolution Equations of Neural Fields Type in a Bounded Domain
Sign Up to like & getrecommendations! Published in 2018 at "Differential Equations and Dynamical Systems"
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
Lipschitz lower semicontinuity moduli for linear inequality systems
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124313
Abstract: Abstract The paper is focussed on the Lipschitz lower semicontinuity of the feasible set mapping for linear (finite and infinite) inequality systems in three different perturbation frameworks: full, right-hand side and left-hand side perturbations. Inspired… read more here.
Keywords: inequality systems; lipschitz lower; lower semicontinuity; semicontinuity moduli ... See more keywords
Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Calculus of Variations"
DOI: 10.1515/acv-2017-0003
Abstract: Abstract We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary order). These results generalize several known lower semicontinuity and relaxation… read more here.
Keywords: growth integral; linear growth; lower semicontinuity; semicontinuity relaxation ... See more keywords