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, R, & KANIA, M (2022). Dissipative mechanism and global attractor for modified Swift-Hohenberg equation in $R^{N}$. Turkish Journal of Mathematics 46 (7): 2728-2750. https://doi.org/10.55730/1300-0098.3298
