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Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level
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 …