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Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems

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  • We consider pulse-like localized solutions for reaction-diffusion systems on a half line and impose various boundary conditions at one end of it. It is shown that the movement of a pulse solution with the homogeneous Neumann boundary condition is completely opposite from that with the Dirichlet boundary condition. As general cases, Robin type boundary conditions are also considered. Introducing one parameter connecting the Neumann and the Dirichlet boundary conditions, we clarify the transition of motions of solutions with respect to boundary conditions.
    Mathematics Subject Classification: Primary: 35K57; Secondary: 35B25, 35K55.

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  • [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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