Life span of solutions of a weakly coupled parabolic system

. We consider the Cauchy problem for the weakly coupled parabolic system ∂ t w λ −Δ w λ = F( w λ ) in R N , where λ > 0, w λ = ( u λ , v λ ), F( w λ ) = ( v λ p , u λ q ) for some p, q ≥ 1, pq > 1, and , for some nonnegative functions φ 1 , φ 2 C 0 ( R N ). If ( p, q ) is sub-critical or eithe...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2008-01, Vol.59 (1), p.1-23
Main Authors: Dickstein, Flávio, Loayza, Miguel
Format: Article
Language:English
Subjects:
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
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Summary:. We consider the Cauchy problem for the weakly coupled parabolic system ∂ t w λ −Δ w λ = F( w λ ) in R N , where λ > 0, w λ = ( u λ , v λ ), F( w λ ) = ( v λ p , u λ q ) for some p, q ≥ 1, pq > 1, and , for some nonnegative functions φ 1 , φ 2 C 0 ( R N ). If ( p, q ) is sub-critical or either φ 1 or φ 2 has slow decay at ∞, w λ blows up for all λ > 0. Under these conditions, we study the blowup of w λ for λ small.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-006-6064-9