Extinction and positivity for the evolution p-Laplacian equation with L1 initial value

The aims of this paper are to discuss extinction and positivity for the evolution p-Laplacian equation ∂u∂t=∂∂x(|∂u∂x|p−2∂u∂x) with initial value u0(x)∈L1(Ω) and zero boundary value conditions, where p>1. In particular, the necessary and sufficient condition for extinction is obtained.