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A Cauchy problem for the hyperbolic modified Swift–Hohenberg equation in RN 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 H2(RN)×L2(RN), which is characterized as the unstable manifold of the set of stationary solutions.
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Czaja et al. (2026) studied this question.
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