Rate of approach to the steady state for a diffusion-convection equation on annular domains

Liping Zhu, Zhengce Zhang
2012 Electronic Journal of Qualitative Theory of Differential Equations  
In this paper, we study the asymptotic behavior of global solutions of the equation ut = ∆u + e |∇u| in the annulus Br,R, u(x, t) = 0 on ∂Br and u(x, t) = M ≥ 0 on ∂BR. It is proved that there exists a constant Mc > 0 such that the problem admits a unique steady state if and only if M ≤ Mc. When M < Mc, the global solution converges in C 1 (Br,R) to the unique regular steady state. When M = Mc, the global solution converges in C(Br,R) to the unique singular steady state, and the blowup rate in
more » ... the blowup rate in infinite time is obtained.
doi:10.14232/ejqtde.2012.1.39 fatcat:z6skvpulwngrtpotzobyvq6sg4