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 our recent work we found a surprising breakdown of symmetry conservation:using standard numerical discretization with very high precision the computednumerical solutions corresponding to very nice initial data may converge tocompletely incorrect steady states due to the gradual accumulation of machineround-off error. We solved this issue by introducing a new Fourier filtertechnique for solutions with certain band gap properties. To furtherinvestigate the attracting basin of steady states we classify in this work allpossible bounded nontrivial steady states for the Allen-Cahn equation. Wecharacterize sharp dependence of nontrivial steady states on the diffusioncoefficient and prove strict monotonicity of the associated energy. Inparticular, we establish a certain self-replicating property amongst thehierarchy of steady states and give a full classification of their energies andprofiles. We develop a new modulation theory and prove sharp convergence to thesteady state with explicit rates and profiles.

Sharp convergence to steady states of Allen-Cahn