Extinction and Positivity of the Solutions for a 𝑝-Laplacian Equation with Absorption on Graphs
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 solu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/937079 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |