Differential and Integral Equations
- Differential Integral Equations
- Volume 18, Number 9 (2005), 961-990.
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 attention is paid to initial data at high energy level; to this end, a basic new idea is to exploit the weak dissipativity (respectively antidissipativity) of the semiflow inside (respectively outside) the Nehari manifold.
Differential Integral Equations, Volume 18, Number 9 (2005), 961-990.
First available in Project Euclid: 21 December 2012
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Gazzola, Filippo; Weth, Tobias. Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level. Differential Integral Equations 18 (2005), no. 9, 961--990. https://projecteuclid.org/euclid.die/1356060117