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Volumn 8, Issue 3, 2003, Pages 279-314

Travelling fronts for monostable reaction-diffusion systems with gradient-dependence

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EID: 33645086748     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (18)

References (43)
  • 1
    • 0003823740 scopus 로고
    • combustion, and nerve propagation, In J.A. Goldstein, editor, "Partial Differential Equations and related Topics," volume 446 of Lecture notes in Mathematics, pages 5-49. Springer, New York
    • D.G. Aronson and H.F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve propagation, In J.A. Goldstein, editor, "Partial Differential Equations and related Topics," volume 446 of Lecture notes in Mathematics, pages 5-49. Springer, New York, 1975.
    • (1975) Nonlinear diffusion in population genetics
    • Aronson, D.G.1    Weinberger, H.F.2
  • 4
    • 0029138236 scopus 로고
    • Algebra, analysis and probability for a coupled system of reaction-diffusion equations
    • A. Champneys, S. Harris, J. Toland, J. Warren, and D. Williams, Algebra, analysis and probability for a coupled system of reaction-diffusion equations, Phil. Trans. R. Soc. Lond. A, 350 (1995), 69-112.
    • (1995) Phil. Trans. R. Soc. Lond. A , vol.350 , pp. 69-112
    • Champneys, A.1    Harris, S.2    Toland, J.3    Warren, J.4    Williams, D.5
  • 5
    • 0003536628 scopus 로고
    • Theory of Ordinary Differential Equations
    • Mc-Graw Hill, New York
    • E.A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," Mc-Graw Hill, New York, 1955.
    • (1955)
    • Coddington, E.A.1    Levinson, N.2
  • 6
    • 0042354357 scopus 로고    scopus 로고
    • On the Vol'pert theory of travelling-wave solutions for parabolic systems
    • E.C.M. Crooks, On the Vol'pert theory of travelling-wave solutions for parabolic systems, Nonlinear Analysis, 26 (1996), 1621-1642.
    • (1996) Nonlinear Analysis , vol.26 , pp. 1621-1642
    • Crooks, E.C.M.1
  • 7
    • 48249136459 scopus 로고    scopus 로고
    • Stability of travelling-wave solutions of reaction-diffusion-convection systems
    • E.C.M. Crooks, Stability of travelling-wave solutions of reaction-diffusion-convection systems, Topological Methods in Nonlinear Analysis, 16 (2000), 37-64.
    • (2000) Topological Methods in Nonlinear Analysis , vol.16 , pp. 37-64
    • Crooks, E.C.M.1
  • 10
    • 0039149429 scopus 로고    scopus 로고
    • Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts
    • U. Ebert and W. van Saarloos, Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts, Physica D, 146 (2000), 1-99.
    • (2000) Physica D , vol.146 , pp. 1-99
    • Ebert, U.1    Van Saarloos, W.2
  • 11
    • 34249762638 scopus 로고
    • The nonlinear stability of front solutions for nonlinear parabolic partial differential equations
    • J.P. Eckmann and C.E. Wayne, The nonlinear stability of front solutions for nonlinear parabolic partial differential equations, Comm. Math. Phys., 161 (1994), 323-334.
    • (1994) Comm. Math. Phys. , vol.161 , pp. 323-334
    • Eckmann, J.P.1    Wayne, C.E.2
  • 12
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to travelling front solutions
    • P.C. Fife and J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Analysis, 65 (1977), 335-361.
    • (1977) Arch. Ration. Mech. Analysis , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 13
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • R.A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), 355-369.
    • (1937) Ann. Eugenics , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 14
    • 0001171846 scopus 로고
    • Local stability of critical fronts in nonlinear parabolic partial differential equations
    • Th. Gallay, Local stability of critical fronts in nonlinear parabolic partial differential equations, Nonlinearity, 7 (1994), 741-764.
    • (1994) Nonlinearity , vol.7 , pp. 741-764
    • Gallay, T.1
  • 16
    • 0016743943 scopus 로고
    • Travelling fronts in nonlinear diffusion equations
    • K.P. Hadeler and F. Rothe, Travelling fronts in nonlinear diffusion equations, J. Math. Biol., 2 (1975), 251-263.
    • (1975) J. Math. Biol. , vol.2 , pp. 251-263
    • Hadeler, K.P.1    Rothe, F.2
  • 17
    • 0003460899 scopus 로고
    • Geometric Theory of Semilinear Equations
    • Lecture Notes in Mathematics, Springer, Berlin
    • D. Henry, "Geometric Theory of Semilinear Equations," volume 840 of Lecture Notes in Mathematics, Springer, Berlin, 1981.
    • (1981) , vol.840
    • Henry, D.1
  • 18
    • 0040241407 scopus 로고
    • Methods in Classical and Functional Analysis
    • Addison-Wesley, Reading, Mass.
    • E. Hille, "Methods in Classical and Functional Analysis," Addison-Wesley, Reading, Mass., 1972.
    • (1972)
    • Hille, E.1
  • 19
    • 0001100679 scopus 로고
    • On the stability of travelling waves in weighted L 8 spaces
    • T. Kapitula, On the stability of travelling waves in weighted L 8 spaces, J. Differential Equations, 112 (1994), 179-215.
    • (1994) J. Differential Equations , vol.112 , pp. 179-215
    • Kapitula, T.1
  • 20
    • 0346449878 scopus 로고    scopus 로고
    • Enhancement of the traveling front speeds in reactiondiffusion equations with advection
    • A. Kiselev and L. Ryzhik, Enhancement of the traveling front speeds in reactiondiffusion equations with advection, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18 (2001), 309-358.
    • (2001) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.18 , pp. 309-358
    • Kiselev, A.1    Ryzhik, L.2
  • 21
    • 0002722044 scopus 로고
    • Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique
    • A.N. Kolmogorov, I. Petrowski, and N. Piscounov, Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Moscow Univ. Math. Bull., 1 (1937), 1-25.
    • (1937) Moscow Univ. Math. Bull. , vol.1 , pp. 1-25
    • Kolmogorov, A.N.1    Petrowski, I.2    Piscounov, N.3
  • 22
    • 0011970475 scopus 로고    scopus 로고
    • Lectures on Elliptic and Parabolic Equations in Hölder Spaces
    • Graduate Studies in Mathematics, American Mathematical Society
    • N.V. Krylov, "Lectures on Elliptic and Parabolic Equations in Hölder Spaces," volume 12 of Graduate Studies in Mathematics, American Mathematical Society, 1996.
    • (1996) , vol.12
    • Krylov, N.V.1
  • 23
    • 0003223550 scopus 로고
    • Linear and Quasilinear Equations of Parabolic Type
    • Translations of Mathematical Monographs, American Mathematical Society, Providence
    • O.A. Ladyženskaja, V.A. Solonnikov, and N.N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," volume 23 of Translations of Mathematical Monographs, American Mathematical Society, Providence, 1968.
    • (1968) , vol.23
    • Ladyženskaja, O.A.1    Solonnikov, V.A.2    Ural'ceva, N.N.3
  • 24
    • 0002820133 scopus 로고
    • Transient bounds and time-asymptotic behavior of solutions to nonlinear equations of Fisher type
    • D.A. Larson, Transient bounds and time-asymptotic behavior of solutions to nonlinear equations of Fisher type, SIAM J. Appl. Math., 34 (1978), 93-103.
    • (1978) SIAM J. Appl. Math. , vol.34 , pp. 93-103
    • Larson, D.A.1
  • 25
    • 0035250586 scopus 로고    scopus 로고
    • The evolution of travelling waves in generalized fisher equations via matched asymptotic expansions: algebraic corrections
    • J.A. Leech and D.J. Needham, The evolution of travelling waves in generalized fisher equations via matched asymptotic expansions: algebraic corrections, Quart. J. Mech. Appl. Math., 54 (2001), 157-175.
    • (2001) Quart. J. Mech. Appl. Math. , vol.54 , pp. 157-175
    • Leech, J.A.1    Needham, D.J.2
  • 26
    • 84894250778 scopus 로고    scopus 로고
    • Spreading speed and linear determinacy for two-species competition models
    • to appear.
    • M.A. Lewis, B. Li, and H.F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., to appear.
    • J. Math. Biol.
    • Lewis, M.A.1    Li, B.2    Weinberger, H.F.3
  • 27
    • 0003963531 scopus 로고
    • Analytic Semigroups and Optimal Regularity in Parabolic Problems
    • Birkhäuser, Basel
    • A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems," Birkhäuser, Basel, 1995.
    • (1995)
    • Lunardi, A.1
  • 28
    • 84980187449 scopus 로고
    • Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov
    • H.P. McKean, Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov, Communs Pure Appl. Math., 28 (1975), 323-331.
    • (1975) Communs Pure Appl. Math. , vol.28 , pp. 323-331
    • McKean, H.P.1
  • 29
    • 1642380986 scopus 로고
    • Travelling waves for mutualist species
    • K. Mischaikow and V. Hutson, Travelling waves for mutualist species, SIAM J. Math. Anal., 24 (1993), 987-1008.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 987-1008
    • Mischaikow, K.1    Hutson, V.2
  • 30
    • 0041149215 scopus 로고
    • A note on the asymptotic behavior of solutions of the KPP equation
    • H.J.K. Moet, A note on the asymptotic behavior of solutions of the KPP equation, SIAM J. Math. Anal., 10 (1979), 728-732.
    • (1979) SIAM J. Math. Anal. , vol.10 , pp. 728-732
    • Moet, H.J.K.1
  • 31
    • 0003475470 scopus 로고
    • Mathematical Biology
    • Biomathematics Text, Springer-Verlag, Berlin
    • J.D. Murray, "Mathematical Biology," volume 19 of Biomathematics Text, Springer-Verlag, Berlin, 1989.
    • (1989) , vol.19
    • Murray, J.D.1
  • 32
    • 0033481359 scopus 로고    scopus 로고
    • Monotonicity and convergence results in order-preserving systems in the presence of symmetry
    • T. Ogiwara and H. Matano, Monotonicity and convergence results in order-preserving systems in the presence of symmetry, Discrete Contin. Dynam. Systems, 5 (1999), 1-34.
    • (1999) Discrete Contin. Dynam. Systems , vol.5 , pp. 1-34
    • Ogiwara, T.1    Matano, H.2
  • 33
    • 0030509749 scopus 로고    scopus 로고
    • Global stability of traveling fronts and convergence towards stacked families of waves in monotone parabolic systems
    • J.-M. Roquejoffre, D. Terman, and V.A. Volpert, Global stability of traveling fronts and convergence towards stacked families of waves in monotone parabolic systems, SIAM J. Math. Anal., 27 (1996), 1261-1269.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1261-1269
    • Roquejoffre, J.-M.1    Terman, D.2    Volpert, V.A.3
  • 34
    • 84971139230 scopus 로고
    • Convergence to travelling fronts in semilinear parabolic equations
    • F. Rothe, Convergence to travelling fronts in semilinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 80 (1978), 213-234.
    • (1978) Proc. Roy. Soc. Edinburgh Sect. A , vol.80 , pp. 213-234
    • Rothe, F.1
  • 35
    • 0000846626 scopus 로고
    • Convergence to pushed fronts
    • F. Rothe, Convergence to pushed fronts, Rocky Mountain J. Math., 11 (1981), 617-633.
    • (1981) Rocky Mountain J. Math. , vol.11 , pp. 617-633
    • Rothe, F.1
  • 36
    • 0000814275 scopus 로고
    • On the stability of waves of nonlinear parabolic systems
    • D.H. Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. Math., 22 (1976), 312-355.
    • (1976) Adv. Math. , vol.22 , pp. 312-355
    • Sattinger, D.H.1
  • 37
    • 0003570325 scopus 로고
    • Non-negative Matrices and Markov Chains
    • Springer-Verlag, Berlin
    • E. Seneta, "Non-negative Matrices and Markov Chains," Springer-Verlag, Berlin, 1981.
    • (1981)
    • Seneta, E.1
  • 38
    • 0035307231 scopus 로고    scopus 로고
    • Partial differential equations of chemotaxis and angiogenisis
    • B.D. Sleeman and H.A. Levine, Partial differential equations of chemotaxis and angiogenisis, Math. Methods Appl. Sci., 24 (2001), 405-426.
    • (2001) Math. Methods Appl. Sci. , vol.24 , pp. 405-426
    • Sleeman, B.D.1    Levine, H.A.2
  • 39
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
    • A. Stevens, The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems, SIAM J. Appl. Math., 61 (2000), 183-212.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 183-212
    • Stevens, A.1
  • 40
    • 0141936308 scopus 로고    scopus 로고
    • Travelling-wave solutions to reaction-diffusion systems of mixed monotone type
    • H. Takase and B.D. Sleeman, Travelling-wave solutions to reaction-diffusion systems of mixed monotone type, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 455 (1999), 1561-1598.
    • (1999) R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. , vol.455 , pp. 1561-1598
    • Takase, H.1    Sleeman, B.D.2
  • 41
    • 0003913993 scopus 로고
    • Travelling-wave Solutions of Parabolic Systems
    • volume 140 of Translations of Mathematical Monographs, American Mathematical Society, Providence, R.I.
    • A.I. Vol'pert, V.A. Vol'pert, and V.A. Vol'pert, "Travelling-wave Solutions of Parabolic Systems," volume 140 of Translations of Mathematical Monographs, American Mathematical Society, Providence, R.I., 1994.
    • (1994)
    • Vol'pert, A.I.1    Vol'pert, V.A.2    Vol'pert, V.A.3
  • 42
    • 84992287989 scopus 로고    scopus 로고
    • Convective instability of reaction fronts: linear stability analysis
    • V.A. Volpert and A.I. Volpert, Convective instability of reaction fronts: linear stability analysis, European J. Appl. Math., 9 (1998), 507-525.
    • (1998) European J. Appl. Math. , vol.9 , pp. 507-525
    • Volpert, V.A.1    Volpert, A.I.2
  • 43
    • 84894273109 scopus 로고    scopus 로고
    • Analysis of the linear determinacy for spread in cooperative models
    • to appear
    • H.F. Weinberger, M.A. Lewis, and B. Li, Analysis of the linear determinacy for spread in cooperative models, J. Math. Biol., to appear.
    • J. Math. Biol.
    • Weinberger, H.F.1    Lewis, M.A.2    Li, B.3


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