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Generalized result with a unified proof of global existence to a class of reaction‐diffusion systems
Author(s) -
Badraoui Salah,
Louafi Hichem
Publication year - 2016
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.3921
Subject(s) - mathematics , reaction–diffusion system , bounded function , domain (mathematical analysis) , class (philosophy) , diffusion , combinatorics , constant (computer programming) , matrix (chemical analysis) , pure mathematics , mathematical physics , mathematical analysis , physics , thermodynamics , chemistry , computer science , chromatography , artificial intelligence , programming language
We prove in this paper a generalized result with a unified proof of global existence in time of classical solutions to a class of a reaction diffusion system with triangular diffusion matrix on a bounded domain inR n . The system in question is u t = a Δ u − f ( x , t , u , v ), v t = c Δ u + d Δ v + ρ f ( x , t , u , v ), x ∈ Ω ⊂ R n ( n ≥ 1 ) , t > 0 with f ( x , t ,0, η ) = 0 and f ( x , t , ξ , η )≤ K φ ( ξ ) e σ η , for all x ∈Ω, t > 0, ξ ≥0, η ≥0; where ρ , K and σ are real positive constants. Copyright © 2016 John Wiley & Sons, Ltd.