2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174479Considering the Cauchy problem for the modified Korteweg-de Vries-Burgers equation $u_t+u_{xxx}+ε|\partial_x|^{2α}u=2(u^{3})_x, u(0)=ϕ$, where $0<ε,α\leq 1$ and $u$ is a real-valued function, we show that it is uniformly globally well-posed in $H^s (s\geq1)$ for all $ε\in (0,1]$. Moreover, we prove that for any $s\geq 1$ and $T>0$, its solution converges in $C([0,T]; H^s)$ to that of the MKdV equation if $ε$ tends to 0.19 pagesAnalysis of PDEs35Q53text