We deal with the extinction of the solutions of the initial-boundary value problem of the discrete p-Laplacian equation with absorption with , , which is said to be the discrete p-Laplacian equation on weighted graphs. For , we show that the nontrivial solution becomes extinction in finite time while it remains strictly positive for , and . Finally, a numerical experiment on a simple graph with standard weight is given.
Qiao Xin. Chunlai Mu. Dengming Liu. "Extinction and Positivity of the Solutions for a -Laplacian Equation with Absorption on Graphs." J. Appl. Math. 2011 1 - 12, 2011. https://doi.org/10.1155/2011/937079