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arXiv · 2511.02341

Local asymptotics for the nonlocal Swift-Hohenberg equation

Elisa Davoli·Christian Kuehn·Luca Scarpa·Lara Trussardi
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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.

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Elisa Davoli, Christian Kuehn, Luca Scarpa, Lara Trussardi. 2025-11-04. Local asymptotics for the nonlocal Swift-Hohenberg equation. https://arxiv.org/abs/2511.02341

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