Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations
The goal of this paper is to investigate the blow-up and the global existence of the solutions to the discrete p-Laplacian parabolic equation utx,t=Δp,wux,t+λux,tp-2ux,t, x,t∈S×0,∞, ux,t=0, x,t∈∂S×0,∞, ux,0=u0, depending on the parameters p>1 and λ>0. Besides, we provide several types of the c...
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Veröffentlicht in: | Discrete Dynamics in Nature and Society 2014-01, Vol.2014 (2014), p.990-999-195 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | The goal of this paper is to investigate the blow-up and the global existence of the solutions to the discrete p-Laplacian parabolic equation utx,t=Δp,wux,t+λux,tp-2ux,t, x,t∈S×0,∞, ux,t=0, x,t∈∂S×0,∞, ux,0=u0, depending on the parameters p>1 and λ>0. Besides, we provide several types of the comparison principles to this equation, which play a key role in the proof of the main theorems. In addition, we finally give some numerical examples which exploit the main results. |
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ISSN: | 1026-0226 1607-887X |
DOI: | 10.1155/2014/716327 |