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Existência de variedade invariante e atrator para a equação ut = uxx + f(u)
(Universidade Federal de São Carlos, 2007-03-26) Teles, Ricardo de Sá; Carbone, Vera Lúcia; https://lattes.cnpq.br/8281633043632854; https://lattes.cnpq.br/1110287669710188
In this work we study the differential equation ut = uxx+ f (u); 0 6 x 6 1; t > 0 with homogeneous Dirichlet boundary conditions and f 2C1(R;R) lipschitz and bounded globally and satisfying the following conditions: (i)limsup juj!¥ f (u)u¡1 6 0 (ii) f (0) = 0: We study the existence of the invariant manifold exponentially attractor decomposing the espace L2(0;1) such that the equation can be rewritten as the weakly coupled system. We use the gradient systems theory to show that the equation has a global attractor.