Trivial Stationary Solutions to the Kuramoto-Sivashinsky and Certain Nonlinear Elliptic Equations

Yanping Cao, Edriss S. Titi

Published 2006-03-30Version 1

We show that the only locally integrable stationary solutions to the integrated Kuramoto-Sivashinsky equation in $R$ and $R^2$ are the trivial constant solutions. We extend our technique and prove similar results to other nonlinear elliptic problems in $\R^N$.