Bifurcation of reaction-diffusion systems: Application to epidemics of many species

Journal of Mathematical Analysis and Applications

Volumn 244, Issue 2, 2000, Pages 542-563

  Leung, Anthony W ^a   Villa, Beatriz R ^b  

^a UNIVERSITY OF CINCINNATI   (United States)

^b UNIVERSIDAD NACIONAL DE COLOMBIA   (Colombia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034654721     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.6737     Document Type: Article

References (14)

1. Blat J., Brown K. J. A reaction-diffusion system modelling the spread of bacterial infections. Math. Methods Appl. Sci. 8:1986;234-246.
2. Capasso V., Maddalena L. A non-linear diffusion system modelling the spread of oro-faecal diseases. Laksmikantham V. Nonlinear Phenomena in Mathematical Sciences. 1981;Academic Press, New York.
3. Capasso V., Maddalena L. Convergence to equilibrium states for a reaction-diffusion system modelling the spread of a class of bacterial and viral diseases. J. Math. Biology. 13:1981;173-184.
4. Crandall M., Rabinowitz P. Bifurcation, perturbation of simple eigenvalues and linearized stability. Arch. Rational Mech. Anal. 52:1973;161-181.
5. Diemling K. Nonlinear Functional Analysis. 1985;Springer-Verlag, New York.
6. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics. 840:1981;Springer-Verlag, New York.
7. Krasnosel'skii M. A. Positive Solutions of Operator Equations. 1964;Noorhoff, Groningen.
8. Leung A. Systems of Nonlinear Partial Differential Equations, Applications to Biology and Engineering. 1989;Kluwer Academic, Boston.
9. Leung A., Villa B. Reaction-diffusion systems for multigroup neutron fission with temperature feedback: Positive steady-state and stability. Differential and Integral Equations. 10:1997;739-756.
10. Leung A., Ortega L. Bifurcating solutions and stabilities for multigroup neutron fission systems with temperature feedback. J. Math. Anal. Appl. 194:1995;489-510.
11. Pao C. V. Nonlinear Parabolic and Elliptic Equations. 1992;Plenum, New York.
12. Pazy A. Semigroup of Linear Operators and Applications to Partial Differential Equations. 1983;Springer-Verlag, New York.
13. Protter M., Weinberger H. Maximum Principles in Differential Equations. 1967;Prentice-Hall, Englewood Cliffs.
14. Stewart B. Generation of analytic semigroups by strongly elliptic operators under general boundary conditions. Trans. Amer. Math. Soc. 259:1980;299-310.