| Abstract: |
| We explicitly construct global attractors for fully nonlinear parabolic
equations in one spatial dimension with two types of phenomena. First,
in case the semiflow is dissipative, the attractor is compact and it can
be decomposed as equilibria and heteroclinic orbits. Second, in case
the semiflow is not dissipative, there are blow-up solutions and the
attractor is unbounded - which can be compactified using an
appropriate Poincar\`e projection with an induced flow at infinity. In this
setting, we view blow-up solutions as heteroclinics orbits to infinity. In
both cases of dissipative and non-dissipative nonlinearities, we state
necessary and sufficient conditions for the occurrence of heteroclinics
between hyperbolic equilibria. The prototype examples are a bounded
and unbounded version of the Chafee-Infante attractor. |
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