Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p-Laplacian with Nonlocal Sources
This paper deals with p-Laplacian systems ut−div(|∇u|p−2∇u)=∫Ωvα(x, t)dx, x∈Ω, t>0, vt−div(|∇v|q−2∇v)=∫Ωuβ(x,t)dx, x∈Ω, t>0, with null Dirichlet boundary conditions in a smooth bounded domain Ω⊂ℝN, where p,q≥2, α,β≥1. We first get the nonexistence result for related elliptic systems of noninc...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/34301 |
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| author | Zhoujin Cui Zuodong Yang |
| author_facet | Zhoujin Cui Zuodong Yang |
| author_sort | Zhoujin Cui |
| collection | DOAJ |
| description | This paper deals with p-Laplacian systems ut−div(|∇u|p−2∇u)=∫Ωvα(x, t)dx, x∈Ω, t>0, vt−div(|∇v|q−2∇v)=∫Ωuβ(x,t)dx, x∈Ω, t>0, with null Dirichlet boundary conditions in a smooth bounded domain
Ω⊂ℝN, where p,q≥2, α,β≥1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=BR={x∈ℝN:|x|<R} (R>0). Then under appropriate hypotheses, we establish local theory of the
solutions and obtain that the solutions either exist globally or blow up in finite time. |
| format | Article |
| id | doaj-art-1312bd7ceae8461e9a06036e1895f33e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1312bd7ceae8461e9a06036e1895f33e2025-02-03T01:32:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/3430134301Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p-Laplacian with Nonlocal SourcesZhoujin Cui0Zuodong Yang1Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, ChinaInstitute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, ChinaThis paper deals with p-Laplacian systems ut−div(|∇u|p−2∇u)=∫Ωvα(x, t)dx, x∈Ω, t>0, vt−div(|∇v|q−2∇v)=∫Ωuβ(x,t)dx, x∈Ω, t>0, with null Dirichlet boundary conditions in a smooth bounded domain Ω⊂ℝN, where p,q≥2, α,β≥1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=BR={x∈ℝN:|x|<R} (R>0). Then under appropriate hypotheses, we establish local theory of the solutions and obtain that the solutions either exist globally or blow up in finite time.http://dx.doi.org/10.1155/2007/34301 |
| spellingShingle | Zhoujin Cui Zuodong Yang Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p-Laplacian with Nonlocal Sources International Journal of Mathematics and Mathematical Sciences |
| title | Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with
p-Laplacian with Nonlocal Sources |
| title_full | Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with
p-Laplacian with Nonlocal Sources |
| title_fullStr | Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with
p-Laplacian with Nonlocal Sources |
| title_full_unstemmed | Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with
p-Laplacian with Nonlocal Sources |
| title_short | Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with
p-Laplacian with Nonlocal Sources |
| title_sort | global existence and blow up solutions and blow up estimates for some evolution systems with p laplacian with nonlocal sources |
| url | http://dx.doi.org/10.1155/2007/34301 |
| work_keys_str_mv | AT zhoujincui globalexistenceandblowupsolutionsandblowupestimatesforsomeevolutionsystemswithplaplacianwithnonlocalsources AT zuodongyang globalexistenceandblowupsolutionsandblowupestimatesforsomeevolutionsystemswithplaplacianwithnonlocalsources |