Extinction and positivity of the solutions for a p-Laplacian equation with absorption on graphs

We deal with the extinction of the solutions of the initial-boundary value problem of the discrete p-laplacian equation with absorption u t = δ p,u - u q with p 1,q 0,which is said to be the discrete p-laplacian equation on weighted graphs. for 0 q 1,we show that the nontrivial solution becomes extinction in finite time while it remains strictly positive for p ≥ 2,q ≥ 1 and q ≥ p - 1. finally,a numerical experiment on a simple graph with standard weight is given. copyright © 2011 qiao xin et al.