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

Considering the Cauchy problem for the modified Korteweg-de Vries-Burgersequation $u_t+u_{xxx}+\epsilon |\partial_x|^{2\alpha}u=2(u^{3})_x, u(0)=\phi$,where $0<\epsilon,\alpha\leq 1$ and $u$ is a real-valued function, we show thatit is uniformly globally well-posed in $H^s (s\geq1)$ for all $\epsilon \in(0,1]$. Moreover, we prove that for any $s\geq 1$ and $T>0$, its solutionconverges in $C([0,T]; H^s)$ to that of the MKdV equation if $\epsilon$ tendsto 0.

Global well-posedness and inviscid limit for the modified Korteweg-de Vries-Burgers equation