Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p -Laplacian with Nonlocal Sources

Zhoujin Cui and Zuodong Yang

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-17

Abstract:

This paper deals with p -Laplacian systems u t − div ( | ∇ u | p − 2 ∇ u ) = ∫ Ω v α ( x , t ) d x , x ∈ Ω , t > 0 , v t − div ( | ∇ v | q − 2 ∇ v ) = ∫ Ω u β ( x , t ) d x , x ∈ Ω ,  t > 0, with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ ℠N , 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 = B R = { x ∈ ℠N : | 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.

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2007/034301.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2007/034301.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:034301

DOI: 10.1155/2007/34301

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().