English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, a partial proof of a conjecture raised by Galaktionov andSvirshchevskii concerning existence and global uniqueness of an asymptoticallystable periodic orbit in a fourth-order piecewise linear ordinary differentialequation is presented. The fourth-order equation comes from the study oftraveling wave patterns in a signed Kuramoto-Sivashinsky equation withabsorption. The proof is twofold. First, the problem of solving for theperiodic orbit is transformed into a zero finding problem in four dimensionalspace, which is solved with a computer-assisted proof based on Newton's methodand the contraction mapping theorem. Second, the rigorous bounds about theperiodic orbit in phase space are combined with the theory of discontinuousdynamical systems to prove that the orbit is asymptotically stable.

Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption