Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity

Jianhua Huang1, Xingfu Zou2
1Department of Mathematics, National University of Defense Technology, Changsha, 410073, China
2Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, A1C5S7, Canada

Tóm tắt

Từ khóa


Tài liệu tham khảo

Britton, N.F. Reaction diffusion equations and their application to biology. Academic Press, New York, 1986

Fife, P.C. Mathematical aspects of reaction and diffusion systems. Lecture Notes in Biomathematics, Vol. 28, Springer-Verlag, Berlin, New York, 1979

Gardner, R. Review on travelling wave solutions of Parabolic Systems by A. I. Volpert, V. A. Volpert and V. A. Volpert. Bull. Amer. Math. Soc., 32: 446–452 (1995)

Gourley, S.A. Wave front solutions of a diffusive delay model for population of Daphnia magna. Comp. Math. Appl., 42: 1421–1430 (2001)

Huang, J., Zou, X. Travelling wavefronts in diffusive and cooperative lotka-volterra system with delays. J. Math. Anal. Appl., 271: 455–466 (2002)

Huang, J., Zou, X. Existence of travelling wavefronts of delayed reaction diffusion systems without monotonicity. Disc. Conti. Dynam. Syst. (series A), 9: 925–936 (2003)

Huang, W. Monotonicity of heteroclinic orbits and spectral properties of variational equations for delay differential equations. J. Differential Equations, 162: 91–139 (2000)

Ma, S. Travelling wavefronts for delayed reaction-diffusion systems via a fixed point theorem. J. Differential Equations, 171: 294–314 (2001)

Murray J. D. Murray. Mathematical Biology, Springer-Verlag, New York, 1989

Pao, C.V. Nonlinear parabolic and elliptic equations. New York, Plenum Press, 1992

Schaaf, K. Asymptotic behavior and travelling wave solutions for parabolic functional differential equations. Trans. Amer. Math. Soc., 302: 587–615 (1987)

Smith, H.L., Thieme, H.R. Monotone semiflows in scalar non-quasimonotone functional differential equations. J. Math. Anal. Appl., 150: 289–306 (1990)

Smith, H.L., Thieme, H.R. Strongly order preserving semiflows generated by functional differential equations. J. Differential Equations, 93: 322–363 (1991)

Smith, H.L., Zhao, X.Q. Global asymptotic stability of travelling waves in delayed reaction-diffusion equations. SIAM J. Math. Anal., 31: 514–534 (2000)

So, J. W.H., Wu, J., Zou, X. A reaction diffusion model for a single species with age structure–I. Travelling wave fronts on unbounded domains. Proc. Royal Soc. London, Ser. A, 457: 1841-1854, 2001

So, J. W.-H., Zou, X. Travelling waves for the diffusive Nicholson’s blowflies equation. Appl. Math. Compt., 122: 385–392 (2001)

Volpert, A.I., Volpert, V.A., Volpert, V.A. Travelling wave solutions of parabolic Systems. Translations of mathematical monographs Vol. 140, Amer. math. Soc., Providence, 1994

Ye, Q., Li, Y. Introduction of reaction diffusion equations. Academy Press, BeiJing, 1985

Wu, J., Zou, X. Travelling wave fronts of reaction diffusion systems with delay. J Dynam. Diff. Eqns., 13(3): 651–687 (2001)

Zeidler, E. Nonlinear functional analysis and its applications, I, Fixed-point Theorems. Springer-Verlag, New York, New York, 1986

Zou, X., Wu, J. Existence of travelling wavefronts in delayed reaction-diffusion system via monotone iteration method. Proc. Amer. Math. Soc., 125: 2589–2598 (1997)