메뉴 건너뛰기




Volumn 455, Issue 1984, 1999, Pages 1561-1598

Travelling-wave solutions to monostable reaction-diffusion systems of mixed monotone type

Author keywords

Autocatalysis; Comparison theorems; Reaction diffusion; Stability; Travelling waves

Indexed keywords


EID: 0141936308     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0372     Document Type: Article
Times cited : (13)

References (29)
  • 3
    • 42149156928 scopus 로고
    • Applications of centre manifold theory
    • Carr, J. 1981 Applications of centre manifold theory. New York: Springer.
    • (1981) New York: Springer.
    • Carr, J.1
  • 4
    • 0019949250 scopus 로고
    • Critical manifolds, travelling waves and an example from population genetics
    • Conley, C. & Fife, P. 1982 Critical manifolds, travelling waves and an example from population genetics. J. Math. Biol. 14, 159-176.
    • (1982) J. Math. Biol. , vol.14 , pp. 159-176
    • Conley, C.1    Fife, P.2
  • 5
    • 0000329668 scopus 로고
    • An application of the generalized Morse index to travelling wave solutions of a competitive reaction diffusion model
    • Conley, C. & Gardner, R. 1989 An application of the generalized Morse index to travelling wave solutions of a competitive reaction diffusion model. Indiana Univ. Math. Jl 33, 319-343.
    • (1989) Indiana Univ. Math. Jl , vol.33 , pp. 319-343
    • Conley, C.1    Gardner, R.2
  • 8
    • 0003299218 scopus 로고
    • Mathematical aspects of reacting and diffusing systems
    • Fife, P. C. 1979 Mathematical aspects of reacting and diffusing systems. In Lecture notes in biomathematics, vol. 28. New York: Springer.
    • (1979) In Lecture Notes in Biomathematics , vol.28
    • Fife, P.C.1
  • 9
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to travelling front solutions
    • Fife, P. C. &: McLeod, J. B. 1977 The approach of solutions of nonlinear diffusion equations to travelling front solutions. Arch. Ration. Mech. Analysis 65, 335-361.
    • (1977) Arch. Ration. Mech. Analysis , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 10
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • Fisher, R. A. 1937 The wave of advance of advantageous genes. Ann. Eugen. 7, 335-369.
    • (1937) Ann. Eugen. , vol.7 , pp. 335-369
    • Fisher, R.A.1
  • 11
    • 84966244631 scopus 로고
    • Stability of travelling wave solution of diffusive predator-prey systems
    • Gardener, R. & Jones, C. 1991 Stability of travelling wave solution of diffusive predator-prey systems. Trans. Am. Math. Soc. 327, 465-524.
    • (1991) Trans. Am. Math. Soc. , vol.327 , pp. 465-524
    • Gardener, R.1    Jones, C.2
  • 13
    • 33746392736 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Henry, D. 1981 Geometric theory of semilinear parabolic equations. New York: Springer.
    • (1981) New York: Springer.
    • Henry, D.1
  • 14
    • 0010250978 scopus 로고
    • Stability in a reaction-diffusion model of mutualism
    • Hutson, V. 1986 Stability in a reaction-diffusion model of mutualism. SIAAI Jl Math. Analysis 17, 58-66.
    • (1986) SIAAI Jl Math. Analysis , vol.17 , pp. 58-66
    • Hutson, V.1
  • 15
    • 0003862232 scopus 로고
    • Perturbation theory for linear operators
    • Kato, T. 1976 Perturbation theory for linear operators. New York: Springer.
    • (1976) New York: Springer.
    • Kato, T.1
  • 17
    • 84971770489 scopus 로고
    • Maximum principles and comparison theorems for semilinear parabolic systems and their applications
    • Lu, G. & Sleeman, B. D. 1993 Maximum principles and comparison theorems for semilinear parabolic systems and their applications. Proc. R. Soc. Edinb. A123, 857-885.
    • (1993) Proc. R. Soc. Edinb. a , vol.123 , pp. 857-885
    • Lu, G.1    Sleeman, B.D.2
  • 18
    • 0000321384 scopus 로고
    • Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension
    • Merkin, J. H. 1993 Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension. Z. Angew. Math. Phys. 44, 707-721.
    • (1993) Z. Angew. Math. Phys. , vol.44 , pp. 707-721
    • Merkin, J.H.1
  • 19
    • 33744882864 scopus 로고
    • The propagation of isothermal reaction diffusion waves in coupled autocatalytic systems
    • Merkin, J. H., Metcalf, M. J., Nccdham, D. J. fe Scott, S. K. 1995 The propagation of isothermal reaction diffusion waves in coupled autocatalytic systems. IMA Jl Appl. Math. 55, 117-133.
    • (1995) IMA Jl Appl. Math. , vol.55 , pp. 117-133
    • Merkin, J.H.1    Metcalf, M.J.2    Nccdham, D.J.3    Scott, S.K.4
  • 20
    • 0028768563 scopus 로고
    • Oscillating wave fronts in isothermal chemical systems with arbitrary powers of autocatalysis
    • Metcalf, M. J., Merkin, J. H. & Scott, S. K. 1994 Oscillating wave fronts in isothermal chemical systems with arbitrary powers of autocatalysis. Proc. R. Soc. Lond. A 447, 155-174.
    • (1994) Proc. R. Soc. Lond. a , vol.447 , pp. 155-174
    • Metcalf, M.J.1    Merkin, J.H.2    Scott, S.K.3
  • 21
    • 1642380986 scopus 로고
    • Travelling waves for mutualist species
    • Mischaikow, K. & Hutson, V. 1993 Travelling waves for mutualist species. SIAM Jl Math. Analysis 24, 987-1008.
    • (1993) SIAM Jl Math. Analysis , vol.24 , pp. 987-1008
    • Mischaikow, K.1    Hutson, V.2
  • 22
    • 0343909748 scopus 로고
    • Travelling waves in predator-prey systems
    • Mischaikow, K. & Reineck, J. 1994 Travelling waves in predator-prey systems. SIAM Jl Math. Analysis 24, 1179-1214.
    • (1994) SIAM Jl Math. Analysis , vol.24 , pp. 1179-1214
    • Mischaikow, K.1    Reineck, J.2
  • 23
    • 0000927953 scopus 로고
    • The effects of geometrical spreading in two and three dimensions on the formation of travelling wavefronts in a simple, isothermal, chemical system
    • Needham, D. J. & Merkin, J. H. 1992 The effects of geometrical spreading in two and three dimensions on the formation of travelling wavefronts in a simple, isothermal, chemical system. Nonlinearity 5, 413-452.
    • (1992) Nonlinearity , vol.5 , pp. 413-452
    • Needham, D.J.1    Merkin, J.H.2
  • 26
    • 0039685238 scopus 로고
    • Weighted norms for the stability of travelling waves
    • Sattinger, D. 1977 Weighted norms for the stability of travelling waves. J. Diff. Eqns 25, 130-144.
    • (1977) J. Diff. Eqns , vol.25 , pp. 130-144
    • Sattinger, D.1
  • 27
    • 84976115095 scopus 로고
    • Comparison principles for strongly coupled reaction-diffusion equations
    • Sleeman, B. D. & Tuma, E. 1987 Comparison principles for strongly coupled reaction-diffusion equations. Proc. R. Soc. Edinb. A106, 209-219.
    • (1987) Proc. R. Soc. Edinb. a , vol.106 , pp. 209-219
    • Sleeman, B.D.1    Tuma, E.2
  • 28
    • 0001526441 scopus 로고
    • The existence of travelling plane waves in a general class of competitiondiffusion systems
    • van Vuuren, J. H. 1995 The existence of travelling plane waves in a general class of competitiondiffusion systems. IMA Jl Appl. Math. 55, 135-148.
    • (1995) IMA Jl Appl. Math. , vol.55 , pp. 135-148
    • Van Vuuren, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.