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Semilinear reaction-diffusion systems with nonlocal sources

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
37
Identifiers
DOI: 10.1016/s0895-7177(03)00109-2
Keywords
  • Reaction-Diffusion Systems
  • Global Existence
  • Finite Time Blowup
  • Nonlocal Sources

Abstract

Abstract This paper investigates the homogeneous Dirichlet boundary value problem u it − δu it = ∏ j=1 n ∫ ω u J P ij dx, i = 1, 2, …, n in a bounded domain Ω ⊂ R N , where pij ≥ 0 (1 ≤ i, j ≤ n) are constants. Denote by I the identity matrix and P = ( pij), which is assumed to be irreducible. It is shown that if I - P is an M-matrix, every nonnegative solution is global, whereas if I - P is not an M-matrix, there exist both global and nonglobal nonnegative solutions.

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