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A Lyapunov functional for a triangular reaction–diffusion system with nonlinearities of exponential growth
Author(s) -
Abdelmalek S.,
Kirane M.,
Youkana A.
Publication year - 2012
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.2572
Subject(s) - mathematics , exponential growth , reaction–diffusion system , lyapunov function , exponential function , exponential stability , diffusion , work (physics) , basis (linear algebra) , mathematical analysis , nonlinear system , geometry , physics , thermodynamics , quantum mechanics
The aim of this work is to study the global existence of solutions to a triangular system of reaction–diffusion equations, which describes epidemiological or chemical situations. On the basis of the construction of a suitable Lyapunov functional, we show that for any initial data, classical global solutions exist even when the nonlinearities are of exponential growth. Copyright © 2012 John Wiley & Sons, Ltd.