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Critical dimension for a system of partial differential equations with time‐dependent generators
Author(s) -
Carmen AndradeGonzález Amanda,
VillaMorales José
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3238
Subject(s) - mathematics , dimension (graph theory) , bounded function , integrable system , laplace operator , partial differential equation , mathematical analysis , pure mathematics , mathematical physics
We give sufficient conditions for blows up of positive mild solutions for the weakly coupled system:∂ u 1∂t= ρ 1tρ 1 − 1Δα 1u 1 + tσ 1u 2β 1,u 10 = ϕ 1 ,∂ u 2∂t= ρ 2tρ 2 − 1Δα 2u 2 + tσ 2u 1β 2,u 20 = ϕ 2 ,whereΔα iis a fractional Laplacian, 0 < α i ≤2, β i ≥1, ρ i >0, σ i >−1 are constants, and the initial condition ϕ i are positive, bounded and integrable functions. We also discuss the critical dimension. Copyright © 2014 John Wiley & Sons, Ltd.