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

Qiao Xin | Zendy; Chunlai Mu | Zendy; Dengming Liu | Zendy

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

Author(s) -

Qiao Xin,

Chunlai Mu,

Dengming Liu

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/937079

Subject(s) - extinction (optical mineralogy) , mathematics , laplace operator , laplacian matrix , absorption (acoustics) , boundary value problem , graph , simple (philosophy) , mathematical analysis , pure mathematics , combinatorics , discrete mathematics , physics , optics , philosophy , epistemology

We deal with the extinction of the solutions of the initial-boundary value problem of the discrete p-Laplacian equation with absorption =Δ,− 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 ≥2, ≥1 and ≥−1. Finally, a numerical experiment on a simple graph with standard weight is given

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