Uniqueness of traveling wave solutions for a biological reaction-diffusion equation

Journal of Mathematical Analysis and Applications

Volumn 316, Issue 1, 2006, Pages 42-59

  Huang, Wenzhang ^a  

^a The University of Alabama in Huntsville   (United States)

Author keywords

Microbial growth in flow reactor; Reaction diffusion equations; Traveling wave solutions; Uniqueness

Indexed keywords

EID: 29944442638     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.04.084     Document Type: Article

References (12)

1. S. Ai, W. Huang, Traveling waves for a reaction-diffusion system in population dynamics and epidemiology, Proc. Roy. Soc. Edinburgh (2005), in press
2. N.T.J. Bailey The Mathematical Theory of Infectious Disease second ed. 1975 Griffin London
3. M. Ballyk D. Le D.A. Jones H.L. Smith Effects of random motility on microbial growth and competition in a flow reactor SIAM J. Appl. Math. 59 1999 573-596
4. Y. Hosono B. Ilyas Existence of traveling waves with any positive speed for a diffusive epidemic model Nonlinear World 1 1994 277-290
5. Y. Hosono B. Ilyas Traveling waves for a simple diffusive epidemic model Math. Models Methods Appl. Sci. 5 1995 935-966
6. W. Huang Traveling waves for a biological reaction-diffusion models J. Dynam. Differential Equations 16 2004 745-766
7. A. Karen Thresholds and traveling waves in an epidemic model for rabies Nonlinear Anal. 8 1984 851-856
8. C.R. Kennedy R. Aris Traveling waves in a simple population model involving growth and death Bull. Math. Biol. 42 1980 397-429
9. C.M. Kung B. Battzis The growth of pure and simple microbial competition in a moving distributed medium Math. Biosci. 111 1992 295-313
10. H.L. Smith X.-Q. Zhao Traveling waves in a bio-reactor model Nonlinear Anal. Real World Appl. 5 2004 895-909
11. A. Volpert V. Volpert V. Volpert Traveling Wave Solutions of Parabolic Systems Transl. Math. Monogr. vol. 40 1994 Amer. Math. Soc.
12. Ya.B. Zel'dovich G.I. Barenblatt V.B. Librovich G.M. Makhviladze The Mathematical Theory of Combustion and Explosions 1985 Consulants Bureau New York