# Science at the triple point between mathematics, mechanics and materials science

## Publication 124

### Slow motion for the 1D Swift-Hohenberg equation

##### Authors:

Gurgen Hayrapetyan
Ohio University
Athens, OH, USA

Matteo Rinaldi
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA, USA

##### Abstract:
The goal of this paper is to study the behavior of certain solutions to the Swift-Hohenberg equation on a one-dimensional torus $\mathbb{T}$. Combining results from $\Gamma$-convergence and ODE theory, it is shown that solutions corresponding to initial data that is $L^1$-close to a jump function $v$, remain close to $v$ for large time. This can be achieved by regarding the equation as the $L^2$-gradient flow of a second order energy functional, and obtaining asymptotic lower bounds on this energy in terms of the number of jumps of $v$.
##### Get the paper in its entirety
16-CNA-005.pdf

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