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Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions
Abstract : We prove local existence of solutions for a class of suitably renormalised coupled SPDE–ODE systems driven by space-time white noise, where the space dimension is equal to 2 or 3. This class includes in particular the FitzHugh–Nagumo system describing the evolution of action potentials of a large population of neurons, as well as models with multidimensional gating variables. The proof relies on the theory of regularity structures recently developed by M. Hairer, which is extended to include situations with semigroups that are not regularising in space. We also provide explicit expressions for the renormalisation constants, for a large class of cubic nonlinearities.
Cited literature [37 references]
https://hal.archives-ouvertes.fr/hal-01141380
Contributor : Nils Berglund Connect in order to contact the contributor
Submitted on : Tuesday, June 16, 2015 - 11:18:33 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:05 PM
Long-term archiving on: : Tuesday, April 25, 2017 - 11:13:56 AM
Contributor : Nils Berglund Connect in order to contact the contributor
Submitted on : Tuesday, June 16, 2015 - 11:18:33 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:05 PM
Long-term archiving on: : Tuesday, April 25, 2017 - 11:13:56 AM
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