Dissipative parabolic equations in locally uniform spaces
2023
Online
Elektronische Ressource
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.
DGES (Spain)
KBN (Poland)
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
TRUE
pub
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Dissipative parabolic equations in locally uniform spaces
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Veröffentlichung: | 2023 |
Medientyp: | Elektronische Ressource |
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