Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A maximum principle for semilinear parabolic systems
HTML articles powered by AMS MathViewer

by Robert H. Martin PDF
Proc. Amer. Math. Soc. 74 (1979), 66-70 Request permission

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.
References
  • H. Amann, Invariant sets for semilinear parabolic and elliptic systems, Equadiff IV (Proc. Czechoslovak Conf. Differential Equations and their Applications, Prague, 1977) Lecture Notes in Math., vol. 703, Springer, Berlin, 1979, pp. 1–4. MR 535316
    • J. S. Griffith, Mathematics of cellular control processes. I. Negative feedback to one gene, J. Theoret. Biol. 20 (1968), 202-208. —, Mathematics of cellular control processes. II. Positive feedback to one gene, J. Theoret. Biol. 20 (1968), 209-216.
  • Roland Lemmert, Über die Invarianz einer konvexen Menge in Bezug auf Systeme von gewöhnlichen, parabolischen und elliptischen Differentialgleichungen, Math. Ann. 230 (1977), no. 1, 49–56 (German). MR 492774, DOI 10.1007/BF01420575
  • J. H. Lightbourne III and R. H. Martin Jr., Relatively continuous nonlinear perturbations of analytic semigroups, Nonlinear Anal. 1 (1976/77), no. 3, 277–292. MR 637076, DOI 10.1016/0362-546X(77)90036-0
  • Robert H. Martin Jr., Asymptotic stability and critical points for nonlinear quasimonotone parabolic systems, J. Differential Equations 30 (1978), no. 3, 391–423. MR 521861, DOI 10.1016/0022-0396(78)90008-6
  • Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
  • Peter Volkmann, Über die positive Invarianz einer abgeschlossenen Teilmenge eines Banachschen Raumes bezüglich der Differentialgleichung $u’=f(t,u)$, J. Reine Angew. Math. 285 (1976), 59–65 (German). MR 415033, DOI 10.1515/crll.1976.285.59
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35K50
  • Retrieve articles in all journals with MSC: 35K50
Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 74 (1979), 66-70
  • MSC: Primary 35K50
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0521875-0
  • MathSciNet review: 521875