Rate of approach to the steady state for a diffusion-convection equation on annular domains
Liping Zhu, Zhengce Zhang · Electronic journal of qualitative theory of differential equations · 2012
In this paper, we study the asymptotic behavior of global solutions of the equation $u_t=\Delta u+e^{| abla u|}$ in the annulus $B_{r,R}$, $u(x,t)=0$ on $\partial B_r$ and $u(x,t)=M\geq 0$ 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