Comparison principles for reaction-diffusion systems with respect to proper polyhedral cones

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Volumn 10, Issue 1-3, 2003, Pages 477-490

  Mincheva, Maya ^a   Siegel, David ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Chemical kinetics; Comparison methods; Cones; Reaction diffusion systems

Indexed keywords

EID: 4644291067     PISSN: 12013390     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (16)

1. H. Amann, Invariant Sets and Existence Theorems for Semilinear Parabolic and Elliptic Systems, J. Math. Anal. Appl., 65, (1978), 432-467.
2. K. H. Chueh, C. C. Conley, J. A. Smoller, Positively Invariant Regions for Systems of Nonlinear Diffusion Equations, Indiana Univ. Math. J., 26 (1977), 373-392.
3. I. Epstein, J. Pojman, An Introduction to Nonlinear Chemical Dynamics, Oxford University Press, Oxford, 1998.
4. H. Kunze, D. Siegel, Monotonicity with respect to Closed Convex Cones I, Dynamics of Continuous, Discrete and Impulsive Systems, 5 (1999), 433-449.
5. H. Kunze, D. Siegel, Monotonicity with respect to Closed Convex Cones II, Appl. Anal., 77 (2001), 233-248.
6. G. S. Ladde, V. Lakshmikantham, A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985.
7. M. Mincheva, D. Siegel, Nonnegativity and Positiveness of Solutions to Reaction-Diffusion Systems Modeling Mass Action Chemical Kinetics, J. Math. Anal. Appl. (submitted)
8. J. D. Murray, Mathematical Biology, Springer-Verlag, Berlin; New York, 1993.
9. M. H. Protter, H. F. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, N.J., 1967.
10. R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
11. St. Scott, Oscillations, Waves and Chaos in Chemical Kinetics, Oxford Science Publications, Oxford, 1994.
12. H. L. Smith, Monotone Dynamical Systems, Introduction to the Theory of the Cooperative and Competitive Systems, American Mathematical Society, Providence, RI, 1995.
13. J. S. Vandergraft, Spectral Properties of Matrices which have Invariant Cones, SIAM J. Appl. Math., 16, No.6, 1968.
14. S. Walcher, On Cooperative Systems with respect to Arbitrary Ordering, J. Math. Anal. Appl., 263 (2001), 543-554.
15. W. Walter, Differential and Integral Inequalities, Springer-Verlag, New York, 1970.
16. R. Webster Convexity, Oxford University Press, Oxford, 1994.