Turkish Journal of Mathematics
Abstract
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.
DOI
10.55730/1300-0098.3298
Keywords
Initial value problems for higher order parabolic equations, Swift-Hohenberg equation, semilinear parabolic equations, dissipative mechanism, global attractor
First Page
2728
Last Page
2750
Recommended Citation
CZAJA, RADOSLAW and KANIA, MARIA
(2022)
"Dissipative mechanism and global attractor for modified Swift-Hohenberg equation in $R^{N}$,"
Turkish Journal of Mathematics: Vol. 46:
No.
7, Article 12.
https://doi.org/10.55730/1300-0098.3298
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss7/12
