Global attractor for the hyperbolic modified Swift–Hohenberg equation in $\mathbb R^N$
Volume 137 / 2026
Annales Polonici Mathematici 137 (2026), 97-130
MSC: Primary 35B41; Secondary 35L25, 35L30, 35L76
DOI: 10.4064/ap251122-11-6
Published online: 3 November 2026
Abstract
A Cauchy problem for the hyperbolic modified Swift–Hohenberg equation in $\mathbb {R}^{N}$ with a mildly integrable potential is considered. It is shown that the equation generates a semigroup of global solutions possessing a compact global attractor in $H^2(\mathbb {R}^N)\times L^2(\mathbb {R}^N)$, which is characterized as the unstable manifold of the set of stationary solutions.
