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/

Zendy Plus

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

Zendy Tools

Zendy Open

We study the initial-boundary value problem for the Hamilton-Jacobi equationwith nonlinear diffusion $u_t=\Delta_p u+|\nabla u|^q$ in a two-dimensionaldomain for $q>p>2$. It is known that the spatial derivative of solutions maybecome unbounded in finite time while the solutions themselves remain bounded.We show that, for suitably localized and monotone initial data, the gradientblow-up occurs at a single point of the boundary. Such a result was known up tonow only in the case of linear diffusion ($p=2$). The analysis in the case$p>2$ is considerably more delicate.

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $p$-Laplacian diffusion