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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We are concerned with the large-time behavior of the radially symmetricsolution for multidimensional Burgers equation on the exterior of a ball$\mathbb{B}_{r_0}(0)\subset \mathbb{R}^n$ for $n\geq 3$ and some positiveconstant $r_0>0$, where the boundary data $v_-$ and the far field state $v_+$of the initial data are prescribed and correspond to a stationary wave. It isshown in \cite{Hashimoto-Matsumura-JDE-2019} that a sufficient condition toguarantee the existence of such a stationary wave is $v_+<0, v_-\leq|v_+|+\mu(n-1)/r_0$. Since the stationary wave is no longer monotonic, itsnonlinear stability is justified only recently in\cite{Hashimoto-Matsumura-JDE-2019} for the case when $v_\pm<0, v_-\leqv_++\mu(n-1)/r_0$. The main purpose of this paper is to verify the timeasymptotically nonlinear stability of such a stationary wave for the wholerange of $v_\pm$ satisfying $v_+<0, v_-\leq |v_+|+\mu(n-1)/r_0$. Furthermore,we also derive the temporal convergence rate, both algebraically andexponentially. Our stability analysis is based on a space weighted energymethod with a suitable chosen weight function, while for the temporal decayrates, in addition to such a space weighted energy method, we also use thespace-time weighted energy method employed in\cite{Kawashima-Matsumura-CMP-1985} and \cite{Yin-Zhao-KRM-2009}.

Asymptotics of Radially Symmetric Solutions for the Exterior Problem of Multidimensional Burgers Equation