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- W1569017997 abstract "This chapter discusses the asymptotic behavior and dynamics of parabolic equations on invariant manifolds. The maximum principle has long been used for various purposes in the study of parabolic equations. There are several other classes of differential equations (ODEs, FDEs, and some parabolic systems) whose semiflows respect an order structure. This naturally calls for an abstraction covering all these equations. In a series of papers from early 80s, Hirsch introduced the notion of monotone dynamical systems and initiated their systematic study. Independently, Matano considered a similar class of semiflows that he called “order preserving.” Triggered by their work, many other researchers contributed to the theory. The monograph of Hess contains several early results dealing with discrete-time systems with special attention to time-periodic parabolic problems. As there are no subharmonic solutions of the scalar ODE, there can be no stable subharmonic solution of the reaction-diffusion equation. On the other hand, for some nonconvex domains, spatially homogeneous equations with linearly stable subharmonic solutions have been constructed." @default.
- W1569017997 created "2016-06-24" @default.
- W1569017997 creator A5044928606 @default.
- W1569017997 date "2002-01-01" @default.
- W1569017997 modified "2023-10-01" @default.
- W1569017997 title "Parabolic Equations: Asymptotic Behavior and Dynamics on Invariant Manifolds" @default.
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