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

Qiao Xin, Chunlai Mu and Dengming Liu

Journal of Applied Mathematics, 2011, vol. 2011, 1-12

Abstract:

We deal with the extinction of the solutions of the initial-boundary value problem of the discrete p -Laplacian equation with absorption ð ‘¢ ð ‘¡ = Δ ð ‘ , 𠜔 ð ‘¢ − ð ‘¢ ð ‘ž 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 ð ‘ â‰¥ 2 , ð ‘ž ≥ 1 and ð ‘ž ≥ ð ‘ âˆ’ 1 . Finally, a numerical experiment on a simple graph with standard weight is given.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:937079

DOI: 10.1155/2011/937079

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