| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4609227 | Journal of Differential Equations | 2017 | 37 Pages |
Abstract
The goal of this paper is to study the behavior of certain solutions to the Swift–Hohenberg equation on a one-dimensional torus TT. Combining results from Γ-convergence and ODE theory, it is shown that solutions corresponding to initial data that is L1L1-close to a jump function v, remain close to v for large time. This can be achieved by regarding the equation as the L2L2-gradient flow of a second order energy functional, and obtaining asymptotic lower bounds on this energy in terms of the number of jumps of v.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
G. Hayrapetyan, M. Rinaldi,