Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610811 | Journal of Differential Equations | 2013 | 48 Pages |
We study the fully nonlinear parabolic equationF(D2um)−ut=0in Ω×(0,+∞),m⩾1, with the Dirichlet boundary condition and positive initial data in a smooth bounded domain Ω⊂RnΩ⊂Rn, provided that the operator F is uniformly elliptic and positively homogeneous of order one. We prove that the renormalized limit of parabolic flow u(x,t)u(x,t) as t→+∞t→+∞ is the corresponding positive eigenfunction which solvesF(D2φ)+μφp=0in Ω, where 0