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Multiple travelling waves for an $SI$-epidemic model
Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems
1. | Institute of Mathematics for Industry, Kyusyu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395 |
2. | Opinion Poll Research Center, The Asahi Shimbun Company, Tokyo 104-8011, Japan |
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J. Carr and R. L. Pego, Metastable patterns in solutions of $u_t = epsilon^2 u_{x x} + f(u)$, Comm. Pure Appl. Math., 42 (1989), 523-576.
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A. Doelman, R. A. Gardner and T. J. Kaper, Stability analysis of singular patterns in the 1-D Gray-Scott model, Physica D, 122 (1998), 1-36.
doi: 10.1016/S0167-2789(98)00180-8. |
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S.-I. Ei, The motion of weakly interacting pulses in reaction-diffusion systems, J. Dynam. Differential Equations, 14 (2002), 85-137.
doi: 10.1023/A:1012980128575. |
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P. C. Fife and J. B. Mcleod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361. |
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doi: 10.1007/BF01048791. |
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K. Kawasaki and T. Ohta, Kink dynamics in one-dimensional nonlinear systems, Physica A, 116 (1982), 573-593.
doi: 10.1016/0378-4371(82)90178-9. |
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show all references
References:
[1] |
J. Carr and R. L. Pego, Metastable patterns in solutions of $u_t = epsilon^2 u_{x x} + f(u)$, Comm. Pure Appl. Math., 42 (1989), 523-576.
doi: 10.1002/cpa.3160420502. |
[2] |
A. Doelman, R. A. Gardner and T. J. Kaper, Stability analysis of singular patterns in the 1-D Gray-Scott model, Physica D, 122 (1998), 1-36.
doi: 10.1016/S0167-2789(98)00180-8. |
[3] |
S.-I. Ei, The motion of weakly interacting pulses in reaction-diffusion systems, J. Dynam. Differential Equations, 14 (2002), 85-137.
doi: 10.1023/A:1012980128575. |
[4] |
P. C. Fife and J. B. Mcleod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361. |
[5] |
G. Fusco and J. Hale, Slow motion manifold, dormant instability and singular perturbations, J. Dynamics and Differential Equations, 1 (1989), 75-94.
doi: 10.1007/BF01048791. |
[6] |
K. Kawasaki and T. Ohta, Kink dynamics in one-dimensional nonlinear systems, Physica A, 116 (1982), 573-593.
doi: 10.1016/0378-4371(82)90178-9. |
[7] |
J. M. Murray, "Mathematical Biology," Springer-Verlag, New York, 1989. |
[8] |
Y. Nishiura, "Far-From-Equilibrium Dynamics," (Translations of Mathematical Monographs), AMS, 2002. |
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