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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/716327 |
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| author | Soon-Yeong Chung |
| author_facet | Soon-Yeong Chung |
| author_sort | Soon-Yeong Chung |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4f318cfa61ef4f09ab883f388da5ace9 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4f318cfa61ef4f09ab883f388da5ace92025-02-03T06:14:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/716327716327Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic EquationsSoon-Yeong Chung0Department of Mathematics and Program of Integrated Biotechnology, Sogang University, Seoul 121-742, Republic of KoreaThe 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.http://dx.doi.org/10.1155/2014/716327 |
| spellingShingle | Soon-Yeong Chung Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations Discrete Dynamics in Nature and Society |
| title | Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations |
| title_full | Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations |
| title_fullStr | Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations |
| title_full_unstemmed | Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations |
| title_short | Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations |
| title_sort | critical blow up and global existence for discrete nonlinear p laplacian parabolic equations |
| url | http://dx.doi.org/10.1155/2014/716327 |
| work_keys_str_mv | AT soonyeongchung criticalblowupandglobalexistencefordiscretenonlinearplaplacianparabolicequations |