Existência de atratores globais para equações de evolução não lineares
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| Autor principal: | |
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| Data de publicació: | 2006 |
| Format: | Master thesis |
| Idioma: | por |
| Font: | Repositório Institucional da UFG |
| Download full: | https://repositorio.bc.ufg.br/tede/handle/tede/14525 |
Sumari: | In this work we develop the theory of global attractor for differential partial equation, denominate evolution equation : ut +2 (ux)2 + uxxx + η(Hux + Huxxx) + μu = f(x), u(., 0) = φ(.) (1) e zt + zzx + zxxx + η(Hzx + Hzxxx) + μz = g(x), z(·, 0) = ψ(·) (2) where H denote the Hilbert transform Hf(x) = 1 πP Z ∞ −∞ f(y) y − x dy, f ∈ S(R), We show that above initial value problem are globally well-possed in Sobolev space. Moreover, we prove existence of global attractor, i.e. invariant set, compact set, which attracts every bounded set of initial conditions. |