| Abstract: |
| In this talk, we analyze the asymptotic behaviour of solutions to the Cauchy problem associated with a class of parabolic equations with critical nonlinearities. We focus on initial data in the energy space $H^1(\mathbb R^N)$ and consider nonlinearities that exhibit critical growth in this energy space. We exploit variational techniques to show that the transition between blow-up in finite time and global existence is determined by the sign of suitable Nehari or Pohozaev functional, at least for low energies solutions. |
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