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Volumn 361, Issue 4, 2009, Pages 2047-2084

Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity

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EID: 64149123850     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-08-04694-1     Document Type: Article
Times cited : (129)

References (48)
  • 1
    • 33750189759 scopus 로고    scopus 로고
    • Traveling wave fronts for generalized Fisher equations with spatio-temporal delays
    • DOI 10.1016/j.jde.2006.08.015, PII S0022039606003354
    • S. Ai, Travelling wave fronts for generalized Fisher equations with spatio-temporal delays, J. Differential Equations 232 (2007), 104-133. MR2281191 (2007h:34052) (Pubitemid 44597103)
    • (2007) Journal of Differential Equations , vol.232 , Issue.1 , pp. 104-133
    • Ai, S.1
  • 2
    • 0036003046 scopus 로고    scopus 로고
    • Travelling fronts for the KPP equation with spatio-temporal delay
    • MR1889183 (2002m:35097)
    • P. B. Ashwin, M. V. Bartuccelli, T. J. Bridges and S. A. Gourley, Travelling fronts for the KPP equation with spatio-temporal delay, Z. Angew. Math. Phys. 53 (2002), 103-122. MR1889183 (2002m:35097)
    • (2002) Z. Angew. Math. Phys. , vol.53 , pp. 103-122
    • Ashwin, P.B.1    Bartuccelli, M.V.2    Bridges, T.J.3    Gourley, S.A.4
  • 3
    • 21144440167 scopus 로고    scopus 로고
    • A nonlocal reaction-diffusion model for a single species with stage structure and distributed maturation delay
    • MR2148679 (2006c:35146)
    • J. F. M. Al-Omari and S. A. Gourley, A nonlocal reaction-diffusion model for a single species with stage structure and distributed maturation delay, Euro. J. Appl. Math. 16 (2005), 37-51. MR2148679 (2006c:35146)
    • (2005) Euro. J. Appl. Math. , vol.16 , pp. 37-51
    • Al-Omari, J.F.M.1    Gourley, S.A.2
  • 4
    • 0346040342 scopus 로고    scopus 로고
    • Dynamics of a strongly nonlocal reaction-diffusion population model
    • DOI 10.1088/0951-7715/17/1/018, PII S0951771504593970
    • J. Billingham, Dynamics of a strongly nonlocal reaction-diffusion population model, Nonlin-earity 17 (2004), 313-346. MR2023445 (2004m:35142) (Pubitemid 38085748)
    • (2004) Nonlinearity , vol.17 , Issue.1 , pp. 313-346
    • Billingham, J.1
  • 5
    • 0025545718 scopus 로고
    • Spatial structures and periodic travelling waves in an integro-deferential reaction-diffusion population model
    • MR1080515 (91m:92020)
    • N.F. Britton, Spatial structures and periodic travelling waves in an integro-deferential reaction-diffusion population model, SIAM J. Appl. Math. 50 (1990), 1663-1688. MR1080515 (91m:92020)
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1663-1688
    • Britton, N.F.1
  • 6
    • 3142699474 scopus 로고    scopus 로고
    • Uniqueness of travelling waves for nonlocal monostable equations
    • DOI 10.1090/S0002-9939-04-07432-5, PII S0002993904074325
    • J. Carr and A. Chmaj, Uniqueness of travelling waves for nonlocal monostable equations, Proc. Amer. Math. Soc. 132 (2004), 2433-2439. MR2052422 (2005b:35125) (Pubitemid 38920297)
    • (2004) Proceedings of the American Mathematical Society , vol.132 , Issue.8 , pp. 2433-2439
    • Carr, J.1    Chmaj, A.2
  • 7
    • 0001203924 scopus 로고    scopus 로고
    • Existence, uniqueness, and asymptotic stability of travelling waves in nonlocal evolution equations, Adv
    • MR1424765 (98f:35069)
    • X. Chen, Existence, uniqueness, and asymptotic stability of travelling waves in nonlocal evolution equations, Adv. Differential Equations 2 (1997), 125-160. MR1424765 (98f:35069)
    • (1997) Differential Equations , vol.2 , pp. 125-160
    • Chen, X.1
  • 8
    • 15444376012 scopus 로고    scopus 로고
    • Existence and uniqueness of entire solutions for a reaction-diffusion equation
    • DOI 10.1016/j.jde.2004.10.028, PII S0022039604004413
    • X. Chen and J. S. Guo, Existence and uniqueness of entire solutions for a reaction-diffusion equation, J. Differential Equations 212 (2005), 62-84. MR2130547 (2006b:35179) (Pubitemid 40398198)
    • (2005) Journal of Differential Equations , vol.212 , Issue.1 , pp. 62-84
    • Chen, X.1    Guo, J.-S.2
  • 9
    • 33846474367 scopus 로고    scopus 로고
    • Entire solutions of reaction-diffusion equations with balanced bistable nonlinearities
    • MR2290131 (2007k:35256)
    • X. Chen, J. S. Guo and H. Ninomiya, Entire solutions of reaction-diffusion equations with balanced bistable nonlinearities, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), 1207-1237. MR2290131 (2007k:35256)
    • (2006) Proc. Roy. Soc. Edinburgh Sect. A , vol.136 , pp. 1207-1237
    • Chen, X.1    Guo, J.S.2    Ninomiya, H.3
  • 10
    • 0003227862 scopus 로고
    • Abstract evolution equations, periodic problems and applications
    • Longman Scientific and Technical, Harlow
    • D. Daners and P. K. McLeod, Abstract evolution equations, periodic problems and applications, Pitman Res. Notes Math. Ser. 279, Longman Scientific and Technical, Harlow, 1992.
    • (1992) Pitman Res. Notes Math. Ser. , vol.279
    • Daners, D.1    McLeod, P.K.2
  • 11
    • 0000360728 scopus 로고
    • On the bounded solutions of a nonlinear convolution equation
    • MR512163 (80c:45015)
    • O. Diekmann and H. G. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Analysis TMA 2 (1978), 721-737. MR512163 (80c:45015)
    • (1978) Nonlinear Analysis TMA , vol.2 , pp. 721-737
    • Diekmann, O.1    Kaper, H.G.2
  • 12
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to traveling wave solutions
    • MR0442480 (56:862)
    • P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling wave solutions, Arch. Rational Mech. Anal. 65 (1977), 335-361. MR0442480 (56:862)
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 13
    • 0019661804 scopus 로고
    • A phase plane discussion of convergence to travelling fronts for nonlinear diffusion
    • MR607901 (83b:35085)
    • P. C. Fife and J. B. McLeod, A phase plane discussion of convergence to travelling fronts for nonlinear diffusion, Arch. Rational Mech. Anal. 75 (1980/1981), 281-314. MR607901 (83b:35085)
    • (1980) Arch. Rational Mech. Anal. , vol.75 , pp. 281-314
    • Fife, P.C.1    McLeod, J.B.2
  • 14
    • 33745920917 scopus 로고    scopus 로고
    • Traveling waves for delayed reaction-diffusion equations with global response
    • MR2189262 (2006i:35182)
    • T. Faria, W. Huang and J. Wu, Traveling waves for delayed reaction-diffusion equations with global response, Proc. R. Soc. Lond. 462A (2006), 229-261. MR2189262 (2006i:35182)
    • (2006) Proc. R. Soc. Lond. , vol.462 A , pp. 229-261
    • Faria, T.1    Huang, W.2    Wu, J.3
  • 15
    • 33745891805 scopus 로고    scopus 로고
    • Nonmonotone travelling waves in a single species reaction-diffusion equation with delay
    • DOI 10.1016/j.jde.2006.05.006, PII S0022039606002002
    • T. Faria and S. Trofimchuk, Nonmonotone travelling waves in a single species reaction-diffusion equation with delay, J. Differential Equations 228 (2006), 357-376. MR2254435 (2007f:35159) (Pubitemid 44041151)
    • (2006) Journal of Differential Equations , vol.228 , Issue.1 , pp. 357-376
    • Faria, T.1    Trofimchuk, S.2
  • 16
    • 15444370248 scopus 로고    scopus 로고
    • Some entire solutions of the Allen-Cahn equation
    • Y. Fukao, Y. Morita and H. Ninomiya, Some entire solutions of the Allen-Cahn equation, Taiwanese J. Math. 8 (2004), 15-32. MR2057634 (2005a:35159) (Pubitemid 41393424)
    • (2004) Taiwanese Journal of Mathematics , vol.8 , Issue.1 , pp. 15-32
    • Fukao, Y.1    Morita, Y.2    Ninomiya, H.3
  • 17
    • 1542616886 scopus 로고    scopus 로고
    • Wavefronts and global stability in a time-delayed population model with stage structure
    • MR1994271 (2004f:92024)
    • S. A. Gourley and Y. Kuang, Wavefronts and global stability in a time-delayed population model with stage structure, Proc. Roy. Soc. Lond. 459A (2003), 1563-1579. MR1994271 (2004f:92024)
    • (2003) Proc. Roy. Soc. Lond. , vol.459 A , pp. 1563-1579
    • Gourley, S.A.1    Kuang, Y.2
  • 18
    • 2442624461 scopus 로고    scopus 로고
    • Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model
    • MR2048407 (2005i:35142)
    • S. A. Gourley and S. Ruan, Convergence and travelling fronts in functional differential equations with nonlocal terms: a competition model, SIAM J. Math. Anal. 35 (2003), 806-822. MR2048407 (2005i:35142)
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 806-822
    • Gourley, S.A.1    Ruan, S.2
  • 19
    • 33745885794 scopus 로고    scopus 로고
    • Nonlocality of reaction-diffusion equations induced by delay: Biological modeling and nonlinear dynamics
    • DOI 10.1023/B:JOTH.0000047249.39572.6d
    • S. A. Gourley, J. H. W. So and J. Wu, Non-locality of reaction-diffusion equations induced by delay: biological modeling and nonlinear dynamics, J. Math. Sci. 124 (2004), 5119-5153. MR2129130 (2006b:35182) (Pubitemid 39470946)
    • (2004) Journal of Mathematical Sciences-New York , vol.124 , Issue.4 , pp. 5119-5153
    • Gourley, S.A.1    So, J.W.2    Wu, J.H.3
  • 20
    • 15444381180 scopus 로고    scopus 로고
    • Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations
    • J. S. Guo and Y. Morita, Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations, Discrete Cont. Dyn. Systems 12 (2005), 193-212. MR2122162 (2006f:35145) (Pubitemid 40419369)
    • (2005) Discrete and Continuous Dynamical Systems , vol.12 , Issue.2 , pp. 193-212
    • Guo, J.-S.1    Morita, Y.2
  • 21
    • 0033431172 scopus 로고    scopus 로고
    • Entire solutions of the KPP Equation
    • MR1699968 (2000e:35088)
    • F. Hamel and N. Nadirashvili, Entire solutions of the KPP Equation, Comm. Pure Appl. Math. LII (1999), 1255-1276. MR1699968 (2000e:35088)
    • (1999) Comm. Pure Appl. Math. LII , pp. 1255-1276
    • Hamel, F.1    Nadirashvili, N.2
  • 23
    • 33646721912 scopus 로고    scopus 로고
    • Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems
    • DOI 10.1088/0951-7715/19/6/003, PII S0951771506006542
    • W. T. Li, G. Lin and S. Ruan, Existence of traveling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems, Nonlinearity 19 (2006), 1253-1273. MR2229998 (2007a:92055) (Pubitemid 43752404)
    • (2006) Nonlinearity , vol.19 , Issue.6 , pp. 1253-1273
    • Li, W.-T.1    Lin, G.2    Ruan, S.3
  • 24
    • 34547272692 scopus 로고    scopus 로고
    • Traveling fronts in diffusive and cooperative Lotka-Volterra system with nonlocal delays
    • MR2341686
    • W. T. Li and Z. C. Wang, Traveling fronts in diffusive and cooperative Lotka-Volterra system with nonlocal delays, Z. angew. Math. Phys. 58 (2007), 571-591. MR2341686
    • (2007) Z. Angew. Math. Phys. , vol.58 , pp. 571-591
    • Li, W.T.1    Wang, Z.C.2
  • 25
    • 84867929521 scopus 로고    scopus 로고
    • Travelling waves and numerical approximations in a reaction advec-tion diffusion equation with nonlocal delayed effects
    • MR1982017 (2004d:92024)
    • D. Liang and J. Wu, Travelling waves and numerical approximations in a reaction advec-tion diffusion equation with nonlocal delayed effects, J. Nonlinear Sci. 13 (2003), 289-310. MR1982017 (2004d:92024)
    • (2003) J. Nonlinear Sci. , vol.13 , pp. 289-310
    • Liang, D.1    Wu, J.2
  • 26
    • 34249880480 scopus 로고    scopus 로고
    • Existence, uniqueness and asymptotic stability of traveling wavefronts in non-local delayed diffusion equation, J
    • MR2333414
    • S. Ma and J. Wu, Existence, uniqueness and asymptotic stability of traveling wavefronts in non-local delayed diffusion equation, J. Dynam. Differential Equations 19 (2007), 391-436. MR2333414
    • (2007) Dynam. Differential Equations , vol.19 , pp. 391-436
    • Ma, S.1    Wu, J.2
  • 27
    • 84966246501 scopus 로고
    • Abstract functional differential equations and reaction-diffusion systems
    • MR967316 (90m:35194)
    • R. H. Martin and H. L. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. Amer. Math. Soc. 321 (1990), 1-44. MR967316 (90m:35194)
    • (1990) Trans. Amer. Math. Soc. , vol.321 , pp. 1-44
    • Martin, R.H.1    Smith, H.L.2
  • 28
    • 33749993458 scopus 로고    scopus 로고
    • Entire solutions with merging fronts to reaction-diffusion equations
    • DOI 10.1007/s10884-006-9046-x
    • Y. Morita and H. Ninomiya, Entire solutions with merging fronts to reaction-diffusion equations, J. Dynam. Differential Equations 18 (2006), 841-861. MR2263404 (2007h:35192) (Pubitemid 44569564)
    • (2006) Journal of Dynamics and Differential Equations , vol.18 , Issue.4 , pp. 841-861
    • Morita, Y.1    Ninomiya, H.2
  • 29
    • 33846855556 scopus 로고    scopus 로고
    • Persistence of wavefronts in delayed non-local reaction diffusion equations
    • MR2309573 (2008c:35151)
    • C. Ou and J. Wu, Persistence of wavefronts in delayed non-local reaction diffusion equations, J. Differential Equations 235 (2007), 216-239. MR2309573 (2008c:35151)
    • (2007) J. Differential Equations , vol.235 , pp. 216-239
    • Ou, C.1    Wu, J.2
  • 31
    • 0002553143 scopus 로고
    • Convergence in smooth strongly monotone flows defined by semilinear parabolic equations
    • MR997611 (90f:58025)
    • P. Poĺacik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. J. Differential Equations 79, 1989: 89-110, MR997611 (90f:58025)
    • (1989) J. Differential Equations , vol.79 , pp. 89-110
    • Poĺacik, P.1
  • 32
    • 0038225098 scopus 로고
    • Domains of attraction of equilibria and monotonicity properties of convergent trajectories in parabolic systems admitting strong comparison principle
    • MR1013724 (90i:58099)
    • P. Poĺa?cik, Domains of attraction of equilibria and monotonicity properties of convergent trajectories in parabolic systems admitting strong comparison principle, J. Reine Angew. Math. 400 (1989), 32-56. MR1013724 (90i:58099)
    • (1989) J. Reine Angew. Math. , vol.400 , pp. 32-56
    • Poĺacik, P.1
  • 34
    • 35348979058 scopus 로고    scopus 로고
    • Spatial-temporal dynamics in nonlocal epidemiological models
    • Y. Iwasa, K. Sato and Y. Takeuchi, eds., Springer-Verlag, New York MR2309365
    • S. Ruan, Spatial-temporal dynamics in nonlocal epidemiological models, in "Mathematics for Life Science and Medicine", Y. Iwasa, K. Sato and Y. Takeuchi, eds., Springer-Verlag, New York, 2007, pp. 99-122. MR2309365
    • (2007) Mathematics for Life Science and Medicine , pp. 99-122
    • Ruan, S.1
  • 35
    • 10044257560 scopus 로고    scopus 로고
    • Stability of steady states and existence of travelling waves in a vector-disease model
    • S. Ruan and D. Xiao, Stability of steady states and existence of traveling waves in a vector disease model, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 991-1011. MR2099575 (2005i:35152) (Pubitemid 39604184)
    • (2004) Royal Society of Edinburgh - Proceedings A , vol.134 , Issue.5 , pp. 991-1011
    • Ruan, S.1    Xiao, D.2
  • 36
    • 0001584326 scopus 로고
    • Asymptotic behavior and travelling wave solutions for parabolic functional differential equations
    • MR891637 (88g:35190)
    • K. W. Schaaf, Asymptotic behavior and travelling wave solutions for parabolic functional differential equations, Trans. Amer. Math. Soc. 302 (1987), 587-615. MR891637 (88g:35190)
    • (1987) Trans. Amer. Math. Soc. , vol.302 , pp. 587-615
    • Schaaf, K.W.1
  • 37
    • 0003270907 scopus 로고
    • Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems
    • Providence, RI MR1319817 (96c:34002)
    • H. L. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Mathematical Surveys and Monographs, 41, Amer. Math. Soc., Providence, RI, 1995. MR1319817 (96c:34002)
    • (1995) Mathematical Surveys and Monographs 41, Amer. Math. Soc.
    • Smith, H.L.1
  • 38
    • 0040807398 scopus 로고    scopus 로고
    • Global asymptotic stability of travelling waves in delayed reaction-diffusion equations
    • MR1740724 (2001c:35239)
    • H. L. Smith and X. Q. Zhao, Global asymptotic stability of travelling waves in delayed reaction-diffusion equations, SIAM J. Math. Anal. 31 (2000), 514-534. MR1740724 (2001c:35239)
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 514-534
    • Smith, H.L.1    Zhao, X.Q.2
  • 40
    • 33845587772 scopus 로고    scopus 로고
    • Monotone travelling fronts of a food-limited population model with nonlocal delay
    • MR2289581 (2007i:35129)
    • Z. C. Wang and W. T. Li, Monotone travelling fronts of a food-limited population model with nonlocal delay, Nonlinear Analysis RWA 8(2007), 699-712. MR2289581 (2007i:35129)
    • (2007) Nonlinear Analysis RWA , vol.8 , pp. 699-712
    • Wang, Z.C.1    Li, W.T.2
  • 41
    • 32044459052 scopus 로고    scopus 로고
    • Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays
    • DOI 10.1016/j.jde.2005.08.010, PII S0022039605003025
    • Z. C. Wang, W. T. Li and S. Ruan, Travelling wave fronts of reaction-diffusion systems with spatio-temporal delays, J. Differential Equations 222 (2006), 185-232. MR2200751 (2006k:35156) (Pubitemid 43192430)
    • (2006) Journal of Differential Equations , vol.222 , Issue.1 , pp. 185-232
    • Wang, Z.-C.1    Li, W.-T.2    Ruan, S.3
  • 42
    • 34249084413 scopus 로고    scopus 로고
    • Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay
    • MR2334595
    • Z. C. Wang, W. T. Li and S. Ruan, Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay, J. Differential Equations 238 (2007), 153-200. MR2334595
    • (2007) J. Differential Equations , vol.238 , pp. 153-200
    • Wang, Z.C.1    Li, W.T.2    Ruan, S.3
  • 43
    • 47149104525 scopus 로고    scopus 로고
    • Traveling fronts in monostable equations with nonlocal delayed effects
    • Z. C. Wang, W. T. Li and S. Ruan, Traveling fronts in monostable equations with nonlocal delayed effects, J. Dynamics and Differential Equations 20 (2008), 563-607.
    • (2008) J. Dynamics and Differential Equations , vol.20 , pp. 563-607
    • Wang, Z.C.1    Li, W.T.2    Ruan, S.3
  • 44
    • 0004201980 scopus 로고
    • Princeton University Press Princeton NJ MR0005923 (3:232d) MR0005923 (3:232d)
    • D. V. Widder, The Laplace transform, Princeton University Press, Princeton, NJ, 1941
    • (1941) The Laplace Transform
    • Widder, D.V.1
  • 46
    • 0343717093 scopus 로고    scopus 로고
    • Traveling wave fronts of reaction-diffusion systems with delay
    • J. Wu and X. Zou, Travelling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations 13 (2001), 651-687. (Erratum, J. Dynam. Differential Equations, DOI: 10.1007/s10884-007-9090-1.) MR1845097 (2003a:35114) (Pubitemid 33808772)
    • (2001) Journal of Dynamics and Differential Equations , vol.13 , Issue.3 , pp. 651-686
    • Wu, J.1    Zou, X.2
  • 47
    • 0037322139 scopus 로고    scopus 로고
    • Backward global solutions characterizing annihilation dynamics of travelling fronts
    • H. Yagisita, Backward global solutions characterizing annihilation dynamics of travelling fronts, Publ. Res. Inst. Math. Sci. 39 (2003), 117-164. MR1935462 (2003h:35142) (Pubitemid 36507503)
    • (2003) Publications of the Research Institute for Mathematical Sciences , vol.39 , Issue.1 , pp. 117-164
    • Yagisita, H.1
  • 48
    • 0037106115 scopus 로고    scopus 로고
    • Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type
    • MR1925963 (2004c:35233)
    • X. Zou, Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type, J. Comp. Appl. Math. 146 (2002), 309-321. MR1925963 (2004c:35233)
    • (2002) J. Comp. Appl. Math. , vol.146 , pp. 309-321
    • Zou, X.1


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