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Dissipative parabolic equations in locally uniform spaces

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Arrieta Algarra, José María y Cholewa, Jan W. y Dlotko, Tomasz y Rodríguez Bernal, Aníbal (2007) Dissipative parabolic equations in locally uniform spaces. Mathematische Nachrichten, 280 (15). pp. 1643-1663. ISSN 0025-584X

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URL Oficial: http://onlinelibrary.wiley.com/doi/10.1002/mana.200510569/pdf


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Resumen

The Cauchy problem for a semilinear second order parabolic equation u(t) = Delta u + f (x, u, del u), (t, x) epsilon R+ x R-N, is considered within the semigroup approach in locally uniform spaces W-U(s,p) (R-N). Global solvability, dissipativeness and the existence of an attractor are established under the same assumptions as for problems in bounded domains. In particular, the condition sf (s, 0) < 0, |s| > s(0) > 0, together with gradient's "subquadratic" growth restriction, are shown to guarantee the existence of an attractor for the above mentioned equation. This result cannot be located in the previous references devoted to reaction-diffusion equations in the whole of R-N.


Tipo de documento:Artículo
Palabras clave:Cauchy problem in RN; Dissipativeness; Global attractor
Materias:Ciencias > Matemáticas > Funciones (Matemáticas)
Código ID:17699
Depositado:16 Ene 2013 10:19
Última Modificación:12 Dic 2018 15:07

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