Local asymptotics for the nonlocal Swift-Hohenberg equation
Analysis of PDEs
2025-11-05 v1
Abstract
The nonlocal-to-local asymptotics investigation for evolutionary problems is a central topic both in the theory of PDEs and in functional analysis. More recently, it became the main core of the mathematical analysis of phase-separation models. In this paper we focus on the Swift-Hohenberg equations which are key benchmark models in pattern formation problems and amplitude equations. We prove well-posedness of the nonlocal Swift-Hohenberg equation, and study the nonlocal-to-local asymptotics with one and two nonlocal contributions under homogeneous Neumann boundary conditions using suitable energy estimates on the nonlocal problems.
Keywords
Cite
@article{arxiv.2511.02341,
title = {Local asymptotics for the nonlocal Swift-Hohenberg equation},
author = {Elisa Davoli and Christian Kuehn and Luca Scarpa and Lara Trussardi},
journal= {arXiv preprint arXiv:2511.02341},
year = {2025}
}