Existência de variedade invariante e atrator para a equação ut = uxx + f(u)
Resumen
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.