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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study in this paper the small data Cauchy problem for the semilineargeneralized Tricomi equations with a nonlinear term of derivative type$u_{tt}-t^{2m}\Delta u=|u_t|^p$ for $m\ge0$. Blow-up result and lifespanestimate from above are established for $1<p\le 1+\frac{2}{(m+1)(n-1)-m}$. If$m=0$, our results coincide with those of the semilinear wave equation. Thenovelty consists in the construction of a new test function, by combiningcut-off functions, the modified Bessel function and a harmonic function.Interestingly, if $n=2$ the blow-up power is independent of $m$. We alsofurnish a local existence result, which implies the optimality of lifespanestimate at least in the $1$-dimensional case.

Blow-up and lifespan estimate for generalized Tricomi equations related to Glassey conjecture