Critical dimension for a system of partial differential equations with time‐dependent generators | Zendy

Carmen AndradeGonzález Amanda | Zendy; VillaMorales José | Zendy

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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.

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