Extinction and Positivity of the Solutions for a p‐Laplacian Equation with Absorption on Graphs
Qiao Xin, Chunlai Mu, Dengming Liu · Journal of Applied Mathematics · 2011
We deal with the extinction of the solutions of the initial‐boundary value problem of the discrete p‐Laplacian equation with absorption ut = Δp,ωu − uq 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.