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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A maximum principle for semilinear parabolic systems

Author: Robert H. Martin
Journal: Proc. Amer. Math. Soc. 74 (1979), 66-70
MSC: Primary 35K50
MathSciNet review: 521875
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Abstract: We develop a criterion insuring that every component of the solution to a system of semilinear parabolic equations is strictly positive for positive time. This criterion involves the strict (component-wise) positiveness of solutions to a related ordinary differentiable system.

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  • [1] H. Amann, Invariant sets and existence theorems for semi-linear parabolic and elliptic systems (to appear). MR 535316 (80h:35074)
  • [2] J. S. Griffith, Mathematics of cellular control processes. I. Negative feedback to one gene, J. Theoret. Biol. 20 (1968), 202-208.
  • [3] -, Mathematics of cellular control processes. II. Positive feedback to one gene, J. Theoret. Biol. 20 (1968), 209-216.
  • [4] R. Lemmert, Über die Invarianz einer konvexen Menge in bezug auf Systeme von gewöhnlichen, parabolischen und elliptischen Differentialgleichungen, Math. Ann. 230 (1977), 49-56. MR 0492774 (58:11841)
  • [5] J. H. Lightbourne and R. H. Martin, Relatively continuous nonlinear perturbations of analytic semigroups, JNA-TMA 1 (1977), 277-292. MR 0637076 (58:30560)
  • [6] R. H. Martin, Jr., Asymptotic stability and critical points for nonlinear quasimonotone parabolic systems, J. Differential Equations (to appear). MR 521861 (80g:35011)
  • [7] M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 0219861 (36:2935)
  • [8] P. Volkmann, Über die positive Invarianz einer abgeschlossenen Teilmenge eines Banachschen Raumes bezüzlich der Differentialgleichung $ u' = f(t,u)$, J. Reine Angew. Math. 285 (1976), 59-65. MR 0415033 (54:3124)

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Keywords: Nonlinear parabolic systems, maximum principle, strict positiveness of solutions
Article copyright: © Copyright 1979 American Mathematical Society

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