Ill posedness of a neural field equation with Heaviside firing rate function

Atribución-NoComercial 4.0 InternacionalCordero Ceballos, Juan CarlosPinilla Estupiñan, Ricardo2019-07-022019-07-022015-07-01ISSN: 2357-6529https://repositorio.unal.edu.co/handle/unal/61887We consider the initial value problem associated to the neural field equationut(x, t) = -u(x, t) + ZRm w(x, y) [1 + g(u(x, t) -u(y, t))] f(u(y, t)) dy, (x, t) Rm x (0, 1),where f is a Heaviside function, then we show that the problem is ill posed in Cb(Rm). The proof follows from a discontinuity argument apply to the equation's flow.application/pdfspaDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/51 Matemáticas / MathematicsIll posedness of a neural field equation with Heaviside firing rate functionArtículo de revistahttp://bdigital.unal.edu.co/60699/info:eu-repo/semantics/openAccessNeural field equationring rate functionsynaptic and sensitive kernelwell and ill posednessflow of the equation.