Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems

Description

We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Lojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico

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Ministerio de Ciencia e Innovación

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Junta de Andalucía

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Ministerio de Educación

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