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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Firstly, we study the equation $\square u = |u|^{q_c}+ |\partial u|^p$ withsmall data, where $q_c$ is the critical power of Strauss conjecture and $p\geqq_c.$ We obtain the optimal lifespan$\ln({T_\varepsilon})\approx\varepsilon^{-q_c(q_c-1)}$ in $n=3$, and improvethe lower-bound of $T_\varepsilon$ from $\exp({c\varepsilon^{-(q_c-1)}})$ to$\exp({c\varepsilon^{-(q_c-1)^2/2}})$ in $n=2$. Then, we study the Cauchyproblem with small initial data for a system of semilinear wave equations$\square u = |v|^q,$ $ \square v = |\partial_t u|^p$ in 3-dimensional spacewith $q<2$. We obtain that this system admits a global solution above a $p-q$curve for spherically symmetric data. On the contrary, we get a new regionwhere the solution will blow up.

Global existence and lifespan for semilinear wave equations with mixed nonlinear terms