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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We construct $C^\infty$ solutions to the one-dimensional nonlinear waveequation $$ u_{tt} - u_{xx} - \tfrac{2(p+2)}{p^2} |u|^p u=0 \quad \text{with}\quad p>0 $$ that blow up on any prescribed uniformly space-like $C^\infty$hypersurface. As a corollary, we show that smooth solutions can blow up (at thefirst instant) on an arbitrary compact set.  We also construct solutions that blow up on general space-like $C^k$hypersurfaces, but only when $4/p$ is not an integer and $k > (3p+4)/p$.

Smooth solutions to the nonlinear wave equation can blow up on Cantor sets