The profile and boundary layer for parabolic system with critical simultaneous blow-up exponent. (September 2016)

• Record Type: Journal Article
• Authors: Liu, Bingchen; Li, Fengjie
• Is Part Of: Applied mathematics letters. Volume 59(2016:Sep.)
• Page Start: 94
• Page End: 100
• Publication Date: 2016-09
• Subjects: Critical simultaneous blow-up exponent -- Uniform blow-up profile -- Boundary layer; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.03.012
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper deals with simultaneous blow-up solutions to a Dirichlet initial–boundary problem of the parabolic equations u t = div ( a ( x ) ∇ u ) + ∫ Ω u m v s d x and v t = div ( b ( x ) ∇ v ) + ∫ Ω u q v p d x in Ω × [ 0, T ) . We complete the previous known results by covering the whole range of possible exponents. Then uniform blow-up profile is obtained for all simultaneous blow-up solutions through proving new rules for some auxiliary systems. At last, boundary layer is studied.