TY - JOUR

T1 - Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations

AU - Poláčik, P.

AU - Yanagida, E.

PY - 2000/12/1

Y1 - 2000/12/1

N2 - Time-periodic reaction-diffusion equations can be discussed in the context of discrete-time strongly monotone dynamical systems. It follows from the general theory that typical trajectories approach stable periodic solutions. Among these periodic solutions, there are some that have the same period as the equation, but, possibly, there might be others with larger minimal periods (these are called subharmonic solutions). The problem of existence of stable subharmonic solutions is therefore of fundamental importance in the study of the behavior of solutions. We address this problem for two classes of reaction diffusion equations under Neumann boundary conditions. Namely, we consider spatially inhomogeneous equations, which can have stable subharmonic solutions on any domain, and spatially homogeneous equations, which can have such solutions on some (necessarily non-convex) domains.

AB - Time-periodic reaction-diffusion equations can be discussed in the context of discrete-time strongly monotone dynamical systems. It follows from the general theory that typical trajectories approach stable periodic solutions. Among these periodic solutions, there are some that have the same period as the equation, but, possibly, there might be others with larger minimal periods (these are called subharmonic solutions). The problem of existence of stable subharmonic solutions is therefore of fundamental importance in the study of the behavior of solutions. We address this problem for two classes of reaction diffusion equations under Neumann boundary conditions. Namely, we consider spatially inhomogeneous equations, which can have stable subharmonic solutions on any domain, and spatially homogeneous equations, which can have such solutions on some (necessarily non-convex) domains.

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M3 - Article

AN - SCOPUS:3042622682

SP - 1

EP - 10

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

SN - 1417-3875

ER -