The profile and boundary layer for parabolic system with critical simultaneous blow-up exponent

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.

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