Inserted: 27 oct 2004
Last Updated: 16 sep 2005
Journal: Diff. Int. Eq.
For a class of semilinear parabolic equations on a bounded domain $\Omega$, we analyze the behavior of the solutions when the initial data varies in the phase space $H^1_0(\Omega)$. We obtain both global solutions and finite time blow-up solutions. Our main tools are the comparison principle and variational methods. Particular attention is paid to initial data at high energy level; to this end, a basic new idea is to use vriational methods, namely exploit the weak dissipativity (resp. antidissipativity) of the semiflow inside (resp. outside) the Nehari manifold.
Keywords: blow-up, global solutions, high energy level