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Volumn 302, Issue 2, 1987, Pages 587-615

Asymptotic behavior and traveling wave solutions for parabolig functional differential equations

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EID: 0001584326     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-1987-0891637-2     Document Type: Article
Times cited : (255)

References (38)
  • 1
    • 0002899831 scopus 로고
    • The asymptotic speed of propagation of a simple epidemic, Nonlinear Diffusion
    • W. E. Fitzgibbon and H. F. Walker, eds.), Pitman, London
    • D. G. Aronson, The asymptotic speed of propagation of a simple epidemic, Nonlinear Diffusion (W. E. Fitzgibbon and H. F. Walker, eds.), Research Notes in Math., no. 14, Pitman, London, 1977, pp. 1-23.
    • (1977) Research Notes in Math., No 14 , pp. 1-23
    • Aronson, D.G.1
  • 2
    • 0002488752 scopus 로고
    • Nonlinear diffusion in population genetics, combustion and nerve propagation, Partial Differential Equations and Related Topics
    • J. Goldstein, ed., Springer-Verlag, Berlin and New York
    • G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion and nerve propagation, Partial Differential Equations and Related Topics (J. Goldstein, ed.), Lecture Notes in Math., vol. 446, Springer-Verlag, Berlin and New York, 1975, pp. 5-49.
    • (1975) Lecture Notes in Math , vol.446 , pp. 5-49
    • Aronson, G.1    Weinberger, H.F.2
  • 3
    • 49349119963 scopus 로고
    • Multidimensional nonlinear diffusion arising in population genetics
    • D. G. Aronson, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978), 33-76.
    • (1978) Adv in Math , vol.30 , pp. 33-76
    • Aronson, D.G.1
  • 5
    • 0003175686 scopus 로고
    • The convergence of solutions of the Kolmogorov equation to travelling waves
    • M. Bramson, The convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Amer. Math. Soc., no. 285, 1983.
    • (1983) Mem. Amer. Math. Soc., No. 285
    • Bramson, M.1
  • 7
    • 0003373629 scopus 로고
    • Non-linear diffusion problems
    • Math. Assoc. Amer., Washington, D. C
    • H. Cohen, Non-linear diffusion problems, Studies in Applied Math., vol. 7, Math. Assoc. Amer., Washington, D. C., 1971.
    • (1971) Studies in Applied Math. , vol.7
    • Cohen, H.1
  • 8
    • 0018184969 scopus 로고
    • Thresholds and travelling waves for the geographical spread of infection
    • O. Diekman, Thresholds and travelling waves for the geographical spread of infection, J. Math. Biol. 6 (1978), 109-130.
    • (1978) J. Math. Biol , vol.6 , pp. 109-130
    • Diekman, O.1
  • 9
    • 84967797244 scopus 로고
    • Run for your life. A note on the asymptotic speed of propagation of an epidemic
    • D. G. Aronson, Run for your life. A note on the asymptotic speed of propagation of an epidemic, Math. Centre, Amsterdam, Report TW 176/78, 1978.
    • (1978) Math. Centre, Amsterdam, Report TW 176/78
    • Aronson, D.G.1
  • 10
    • 0003299218 scopus 로고
    • Mathematical aspects of reacting and diffusing systems
    • Springer-Verlag, Berlin and New York
    • P. C. Fife, Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomath., vol. 28, Springer-Verlag, Berlin and New York, 1979.
    • (1979) Lecture Notes in Biomath. , vol.28
    • Fife, P.C.1
  • 11
    • 84968501796 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to travelling wave solutions
    • P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling wave solutions, Bull. Amer. Math. Soc. 81 (1975), 1076-1078
    • (1975) Bull. Amer. Math. Soc , vol.81 , pp. 1076-1078
    • Fife, P.C.1    McLeod, J.B.2
  • 13
    • 0019661804 scopus 로고
    • A phase plane discussion of convergence to travelling fronts for nonlinear diffusion, Arch
    • D. G. Aronson, A phase plane discussion of convergence to travelling fronts for nonlinear diffusion, Arch. Rational Mech. Anal. 75 (1981), 281-314.
    • (1981) Rational Mech. Anal , vol.75 , pp. 281-314
    • Aronson, D.G.1
  • 15
    • 79951902115 scopus 로고
    • Introduction to the theory of linear nonself adjoint operators
    • Amer. Math. Soc., Providence, R. I
    • C. Gohberg and M. G. Krein, Introduction to the theory of linear nonself adjoint operators, Transi. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R. I., 1969.
    • (1969) Transi. Math. Monographs , vol.18
    • Gohberg, C.1    Krein, M.G.2
  • 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
    • 0003346959 scopus 로고
    • Theory of functional differential equations
    • SpringerVerlag, Berlin and New York
    • J. Hale, Theory of functional differential equations, 2nd ed., Appl. Math. Sei., vol. 3, SpringerVerlag, Berlin and New York, 1977.
    • (1977) Appl. Math. Sei. , vol.3
    • Hale, J.1
  • 18
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer-Verlag, Berlin and New York
    • D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer-Verlag, Berlin and New York, 1981.
    • (1981) Lecture Notes in Math. , vol.840
    • Henry, D.1
  • 19
    • 33746834515 scopus 로고
    • Biological growth and spread (Proc. Heidelberg 1979)
    • Springer-Verlag, Berlin and New York
    • W. Jäger, H. Rost, and P. Tautu (eds), Biological growth and spread (Proc. Heidelberg 1979), Lecture Notes in Biomath., vol. 38, Springer-Verlag, Berlin and New York, 1980.
    • (1980) Lecture Notes in Biomath. , vol.38
    • Jäger, W.1    Rost, H.2    Tautu, P.3
  • 20
    • 84957345012 scopus 로고
    • On the nonlinear diffusion equations of Kolmogorov-Petrovsky-Piskunov type, Osaka
    • Y. Kametaka, On the nonlinear diffusion equations of Kolmogorov-Petrovsky-Piskunov type, Osaka J. Math. 13 (1976), 11-66.
    • (1976) J. Math , vol.13 , pp. 11-66
    • Kametaka, Y.1
  • 21
    • 0000638913 scopus 로고
    • Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory
    • Ja. I. Kanel', Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory, Mat. Sb. (N.S.) 59(101) (1962), 245-288.
    • (1962) Mat. Sb. (N.S.) , vol.59 , Issue.101 , pp. 245-288
    • Kanel, J.A.1
  • 22
    • 0003913874 scopus 로고
    • On the stability of solutions of the equation of combustion theory for finite initial functions, Mat
    • D. G. Aronson, On the stability of solutions of the equation of combustion theory for finite initial functions, Mat. Sb. (N.S.) 65(107) (1964), 398-413.
    • (1964) Sb (NS) , vol.65 , Issue.107 , pp. 398-413
    • Aronson, D.G.1
  • 24
    • 84972539437 scopus 로고
    • On the semilinear heat equation with time-lag, Hiroshima
    • K. Kobayashi, On the semilinear heat equation with time-lag, Hiroshima Math. J. 7 (1977), 459-472.
    • (1977) Math. J , vol.7 , pp. 459-472
    • Kobayashi, K.1
  • 25
    • 0002722044 scopus 로고
    • Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, MoscowUniv. Bull
    • A. N. Kolmogoroff, I. G. Petrovski, and N. S. Piskunoff, Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Moscow Univ. Bull. Math., Série Internat., Sec. A, Math, et Méc. 1(6) (1937), 1-25.
    • (1937) Math., Série Internat., Sec. A, Math, Et Méc , vol.1 , Issue.6 , pp. 1-25
    • Kolmogoroff, A.N.1    Petrovski, I.G.2    Piskunoff, N.S.3
  • 26
    • 84980187449 scopus 로고
    • Application of Brownian motion to the equation of Kolmogorov- Petrovskii-Piskunov, Comm. Pure Appl
    • H. P. McKean, Application of Brownian motion to the equation of Kolmogorov- Petrovskii-Piskunov, Comm. Pure Appl. Math. 28 (1975), 323-331.
    • (1975) Math , vol.28 , pp. 323-331
    • McKean, H.P.1
  • 27
    • 34250288089 scopus 로고
    • Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Funktionalen
    • R. Redheffer and W. Walter, Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Funktionalen, Math. Ann. 226 (1977), 155-170.
    • (1977) Math. Ann , vol.226 , pp. 155-170
    • Redheffer, R.1    Walter, W.2
  • 28
    • 84971139230 scopus 로고
    • Convergence to travelling fronts in semilinearparabolic 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
  • 29
    • 0000814275 scopus 로고
    • On the stability of travelling waves
    • D. Sattinger, On the stability of travelling waves, Adv. in Math. 22 (1976), 312-355.
    • (1976) Adv.In Math. , vol.22 , pp. 312-355
    • Sattinger, D.1
  • 30
    • 84967709919 scopus 로고
    • Weighted norms for the stability of travelling waves
    • D. G. Aronson, Weighted norms for the stability of travelling waves, J. Differential Equations 25 (1977), 179-201.
    • (1977) J. Differential Equations , vol.25 , pp. 179-201
    • Aronson, D.G.1
  • 31
    • 0346621911 scopus 로고
    • Travelling-front solutions for integro-differential equations. I
    • K. Schumacher, Travelling-front solutions for integro-differential equations. I, J. Reine Angew. Math. 316 (1980), 54-70.
    • (1980) J. Reine Angew. Math , vol.316 , pp. 54-70
    • Schumacher, K.1
  • 32
    • 0012666175 scopus 로고
    • Travelling-front solutions of integro-differential equations
    • Springer-Verlag, Berlin and New York
    • D. G. Aronson, Travelling-front solutions of integro-differential equations. II, Lecture Notes in Biomath., vol. 38, Springer-Verlag, Berlin and New York, 1980, pp. 296-309.
    • (1980) Lecture Notes in Biomath , vol.38 , pp. 296-309
    • Aronson, D.G.1
  • 33
    • 2042426692 scopus 로고
    • Strong maximum principle for non-linear parabolic differential-functional inequalities in arbitrary domains
    • J. Szarski, Strong maximum principle for non-linear parabolic differential-functional inequalities in arbitrary domains, Ann. Polon. Math. 31 (1975), 197-203.
    • (1975) Ann. Polon. Math , vol.31 , pp. 197-203
    • Szarski, J.1
  • 34
    • 0008260279 scopus 로고
    • Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations
    • H. Thieme, Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations, J. Reine Angew. Math. 306 (1979), 94-121.
    • (1979) J. Reineangew. Math , vol.306 , pp. 94-121
    • Thieme, H.1
  • 35
    • 0000027176 scopus 로고
    • The behavior of solutions of some nonlinear diffusion equations for large time
    • K. Uchiyama, The behavior of solutions of some nonlinear diffusion equations for large time, J. Math. Kyoto Univ. 18 (1978), 453-508.
    • (1978) J. Math , vol.18 , pp. 453-508
    • Uchiyama, K.1
  • 37
    • 84963120856 scopus 로고
    • Asymptotic behavior of a class of discrete time models in population genetics
    • V. Lakshmikantham, ed.), Academic Press
    • H. F. Weinberger, Asymptotic behavior of a class of discrete time models in population genetics, Applied Nonlinear Analysis (V. Lakshmikantham, ed.), Academic Press, 1979, pp. 407-422.
    • (1979) Applied Nonlinear Analysis , pp. 407-422
    • Weinberger, H.F.1
  • 38
    • 0141708537 scopus 로고
    • The linear difference-differential equation with asymptotically constant coefficients, Amer
    • M. Wright, The linear difference-differential equation with asymptotically constant coefficients, Amer. J. Math. 70 (1948), 221-238.
    • (1948) J. Math , vol.70 , pp. 221-238
    • Wright, M.1


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