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Necessary conditions for positivity-preserving property of reaction-diffusion systems with delay.
Electron. J. Qual. Theory Differ. Equations 13, 1-7 (2016)
We consider the reaction-diffusion system with delay {partial derivative u/partial derivative t = A (t, x)Delta u - Sigma(k)(i=1) gamma(i) (t, x)partial derivative(xi) u + f(t, u(t)), x is an element of Omega; B(u)vertical bar(partial derivative Omega) = 0. We show that this system with delay preserves positivity if and only if its diffusion matrix A and convection matrix gamma(i) are diagonal with non-negative elements and nonlinear delay term f satisfies the normal tangential condition.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Positivity ; Monotonicity ; Reaction-diffusion Equation With Delay; Functional-differential Equations; 3-dimensional Systems; Convergence; Invariance; Sets
e-ISSN
1417-3875
Quellenangaben
Volume: 13,
Pages: 1-7
Publisher
Szeged University
Publishing Place
Szeged
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)