Extinction and Positivity of the Solutions for a p-Laplacian Equation with Absorption on Graphs

الملخص EN

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.