RT Journal Article
T1 Dissipative parabolic equations in locally uniform spaces
A1 Arrieta Algarra, José María
A1 Cholewa, Jan W.
A1 Dlotko, Tomasz
A1 Rodríguez Bernal, Aníbal
AB 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.
PB Wiley-Blackwell
SN 0025-584X
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/50285
UL https://hdl.handle.net/20.500.14352/50285
LA eng
NO DGES (Spain)
NO KBN (Poland)
DS Docta Complutense
RD 12 may 2025