| Abstract: |
| We provide a relation between the well known class of dissipative equations and the recently introduced class of slowly non-dissipative equations, in the setting of scalar reaction-diffusion equations. The latter type of equations is characterized by the existence of grow-up (i.e., in finite time blow-up) with absence of finite time blow-up. A particular small perturbation of an unbounded non-dissipative global attractor is considered, in such a way that the perturbed attractor is dissipative. Although the continuity of the family of attractors is veri fied in compact sets, our choice of perturbation produces a great change on the dynamics close to the in finity of the phase space. In other words, we prove that the limit of the compact attractors is not the unbounded attractor of the limiting equation. |
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