Biblioteca de la Universidad Complutense de Madrid

Minimal periods of semilinear evolution equations with Lipschitz nonlinearity

Impacto



Robinson, James C. y Vidal López, Alejandro (2006) Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. Journal of Differential Equations, 220 (2). pp. 396-406. ISSN 0022-0396

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URL Oficial: http://www.sciencedirect.com/science/journal/00220396



Resumen

It is known that any periodic orbit of a Lipschitz ordinary differential equation must have period at least 2π/L, where L is the Lipschitz constant of f. In this paper, we prove a similar result for the semilinear evolution equation du/dt=-Au+f(u): for each α with 0 α 1/2 there exists a constant Kα such that if L is the Lipschitz constant of f as a map from D(Aα) into H then any periodic orbit has period at least KαL-1/(1-α). As a concrete application we recover a result of Kukavica giving a lower bound on the period for the 2d Navier–Stokes equations with periodic boundary conditions.


Tipo de documento:Artículo
Palabras clave:Period orbits; Minimal period; Semilinear evolution equations; Navier–Stokes equations
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:12584
Depositado:13 Abr 2011 08:37
Última Modificación:06 Feb 2014 09:27

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