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

Stabilization towards the steady state for a viscous Hamilton-Jacobi equation

Abstract Related Papers Cited by
  • In this short paper, we obtain the asymptotic behavior of the global solutions of a viscous Hamilton-Jacobi equation $u_t=\Delta u+|\nabla u|^p$ in $B_{r,R}$, $u(x,t)=0$ on $\partial B_r$ and $u(x,t)=M$ on $\partial B_R$. It is proved that there exists a constant $M_c>0$ such that the problem admits a unique steady state if and only if $M\leq M_c$. When $M < M_c$, the global solution converges in $C^1(\overline{B_{r,R}})$ to the unique regular steady state. When $M=M_c$, the global solution converges in $C(\overline{B_{r,R}})$ to the unique singular steady state, and the grow-up rate of $||u_\nu(t)||_{L^\infty(\partial B_r)}$ in infinite time is obtained.
    Mathematics Subject Classification: Primary: 35K60, 35K65, 35B45.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(90) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return