A nonexistence result for a nonlinear PDE with Robin condition

Brahim Khodja

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-12

Abstract:

Under the assumption λ > 0 and f verifying f ( x , y , 0 ) = 0 in D , 2 F ( x , y , u ) − u f ( x , y , u ) ≥ 0 , u ≠0 , and if Ω = R × D , we show the convexity of function E ( t ) = ∬ D | u ( t , x , y ) | 2 d x d y , where u : Ω → ℠is a solution of problem λ ( ∂ 2 u / ∂ t 2 ) − ( ∂ / ∂ x ) ( p ( x , y ) ( ∂ u / ∂ x ) ) − ( ∂ / ∂ y ) ( q ( x , y ) ( ∂ u / ∂ y ) ) + f ( x , y , u ) = 0  in Ω , u + ε ( ∂ u / ∂ n ) = 0  on  ∂ Ω , considered in H 2 ( Ω ) ∩ L ∞ ( Ω ) , p , q : D ¯ → ℠are two nonnull functions on D , ε is a positive real number, and D = ] a 1 , b 1 [ × ] a 2 , b 2 [ , ( F ( x , y , s ) = ∫ 0 s f ( x , y , t ) d t ) .

Date: 2006
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2006/062601.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2006/062601.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:062601

DOI: 10.1155/IJMMS/2006/62601

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 ().