\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half plane

Abstract Related Papers Cited by
  • We investigate the asymptotic stability of a stationary solution to an initial boundary value problem for a 2-dimensional viscous conservation law in half plane. Precisely, we show that under suitable boundary and spatial asymptotic conditions, a solution converges to the corresponding stationary solution as time tends to infinity. The proof is based on an a priori estimate in the $H^2$-Sobolev space, which is obtained by a standard energy method. In this computation, we utilize the Poincaré type inequality. In addition, we obtain a convergence rate under the assumption that the initial data converges to a spatial asymptotic state algebraically fast. This result is obtained by a weighted energy estimate.
    Mathematics Subject Classification: Primary 35L65, 35L67, 76L05.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
Open Access Under a Creative Commons license
SHARE

Article Metrics

HTML views() PDF downloads(108) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return