一类非线性快速扩散方程解的熄灭

摘要

We prove global existence and gradient estimates to the initial boundary problems for the quasi-linear parabolic equations in with the initial-boundary conditions and. where is a bounded domain in , is a function like ,and is a nonlinear perturbation like . Under the assumptions that the mean curvature of is non-positive and is small, we derive in particular an precise estimate for which include both of a smoothing effect and a decay property.%证明了一类如下抛物方程解的爆破pmt u uu div u=(∇-1∇)+λ， x∈Ω， t>0其中Ω是RN的有界区域。当参数满足一定条件时解在有限时刻爆破。