Dissipative mechanism and global attractor for modified Swift-Hohenberg equation in
A Cauchy problem for a modification of the Swift-Hohenberg equation in $ R^{N} $ with a
mildly integrable potential is considered. Applying the dissipative mechanism of fourth order
parabolic equations in unbounded domains, it is shown that the equation generates a
semigroup of global solutions possessing a global attractor in the scale of Bessel potential
spaces and in $ H^ 2 (R^{N}) $ in particular.
mildly integrable potential is considered. Applying the dissipative mechanism of fourth order
parabolic equations in unbounded domains, it is shown that the equation generates a
semigroup of global solutions possessing a global attractor in the scale of Bessel potential
spaces and in $ H^ 2 (R^{N}) $ in particular.
Abstract
A Cauchy problem for a modification of the Swift-Hohenberg equation in with a mildly integrable potential is considered. Applying the dissipative mechanism of fourth order parabolic equations in unbounded domains, it is shown that the equation generates a semigroup of global solutions possessing a global attractor in the scale of Bessel potential spaces and in in particular.
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