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arXiv · 2109.04515

Existence, Regularity, and a Strong It\^o Formula for the Isochronal Phase of SPDE

Zachary P. Adams
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Abstract

We prove the existence and regularity of the isochron map for stable invariant manifolds of a large class of evolution equations. Our results apply in particular to the isochron map of reaction-diffusion equations and neural field equations. Using the regularity properties proven here, we are able to obtain a strong It\^o formula for the isochronal phase of stochastically perturbed travelling waves, spiral waves, and other patterns appearing in SPDEs driven by white noise, even for SPDEs that only admit mild solutions.

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Zachary P. Adams. 2021-09-09. Existence, Regularity, and a Strong It\^o Formula for the Isochronal Phase of SPDE. https://arxiv.org/abs/2109.04515

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