Well-posedness of the stochastic neural field equation with discontinuous firing rate

DOI10.1007/S00028-017-0409-ZzbMath1396.35079OpenAlexW2755421927MaRDI QIDQ1670257

Peng Zhang

Publication date: 5 September 2018

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-017-0409-z

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Integro-partial differential equations (35R09)

Related Items (3)

Asymptotic behavior of a neural field lattice model with a heaviside operator ⋮ Sigmoidal approximations of Heaviside functions in neural lattice models ⋮ A gradient flow formulation for the stochastic Amari neural field model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(L^{2}\)-stability of traveling wave solutions to nonlocal evolution equations
• Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity
• Random perturbation of PDEs and fluid dynamic models. École d'Été de Probabilités de Saint-Flour XL -- 2010
• Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis
• Mathematical foundations of neuroscience
• Measures of noncompactness and condensing operators. Transl. from the Russian by A. Iacob
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Large deviations for nonlocal stochastic neural fields
• Stochastic neural field equations: a rigorous footing
• Waves, bumps, and patterns in neural field theories
• Reaction-Diffusion Equations with Spatially Distributed Hysteresis
• Spatiotemporal dynamics of continuum neural fields
• A Note on a Result of Liptser-Shiryaev
• The monotone iterative technique for a parabolic boundary value problem with discontinuous nonlinearity
• Existence and properties of solutions for neural field equations
• A step-function model in chemical reactor theory: multiplicity and stability of solutions
• A note on uniqueness for parabolic problems with discontinuous nonlinearities
• The obstacle problem and partial differential equations with discontinuous nonlinearities
• Evans Functions for Integral Neural Field Equations with Heaviside Firing Rate Function
• Neural Fields
• On the uniqueness and non‐uniqueness of solutions of initial value problems for some quasi‐linear parabolic equations
• Uniqueness and Absolute Continuity for Semilinear SPDE’s
• Stochastic Equations in Infinite Dimensions

This page was built for publication: Well-posedness of the stochastic neural field equation with discontinuous firing rate