Behavior of solutions of Burgers's equation with nonlocal boundary conditions. II

Keng Deng
1994 Quarterly of Applied Mathematics  
We study the large-time behavior of positive solutions of Burgers's equation ut = uxx + euux, 0 < x < 1, t > 0 (e > 0), subject to the nonlocal boundary condition: -ux(0,t)-jeu2{0,t) = at/(0, t)(f0' u(x, t)dx)q , u(l, t) = 0 (0 < p, q < oo). The steady-state problem is analyzed in detail, and the result about finite-time blow-up is proved. where the model problems are f{u) -\eu2 and g{u, v) = aupvq or g(u, v) = at/vq -f(u).
doi:10.1090/qam/1292205 fatcat:zhawyejtljehxozdifqapt4lfe