一类具有非线性迁移项的拟线性抛物方程解的熄灭

The Quenching Phenomena for a Quasilinear Parabolic Equation with a Nonlinear Convection Term

在Rn有界域上讨论了具有非线性迁移项的平均曲率型方程ut-div[σ(| u|2) u]+b(u)· u=0的初边值问题。若初值u0∈Lq,q≥n,问题的解将在有限时刻熄灭,并且给出了解的L∞估计。

Deriving the quenching phenomena to an initial-boundary value problem in a bounded domain in the R^n for the mean curvature equation with a nonlinear convection term:u_t-div｛σ(|u|~2)u｝+b(u)·u=0. If u_0∈L^q,q≥n,the solution will quench in limit time.We also give the L~∞-estimate.