2026-06-27T10:18:59Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/502852023-08-25T10:22:01Zcom_20.500.14352_14col_20.500.14352_15

Arrieta Algarra, José María Cholewa, Jan W. Dlotko, Tomasz Rodríguez Bernal, Aníbal 2023-06-20T09:44:37Z 2023-06-20T09:44:37Z 2007 0025-584X 10.1002/mana.200510569 https://hdl.handle.net/20.500.14352/50285 http://onlinelibrary.wiley.com/doi/10.1002/mana.200510569/pdf http://onlinelibrary.wiley.com/ 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. eng restricted access Dissipative parabolic equations in locally uniform spaces journal article