Submitted Paper

Inserted: 5 nov 2025
Last Updated: 5 nov 2025

Year: 2025

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: well-posedness, nonlocal-to-local convergence, Swift-Hohenberg equation

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• Davoli-Kuehn-Scarpa-Trussardi.pdf