Ill posedness of a neural field equation with Heaviside firing rate function
We 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 arg...
- Autores:
-
Cordero Ceballos, Juan Carlos
Pinilla Estupiñan, Ricardo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2015
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/61887
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/61887
http://bdigital.unal.edu.co/60699/
- Palabra clave:
- 51 Matemáticas / Mathematics
Neural field equation
ring rate function
synaptic and sensitive kernel
well and ill posedness
flow of the equation.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | We 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. |
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