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2005 Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level
Filippo Gazzola, Tobias Weth
Differential Integral Equations 18(9): 961-990 (2005).

Abstract

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.

Citation

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Filippo Gazzola. Tobias Weth. "Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level." Differential Integral Equations 18 (9) 961 - 990, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35248
MathSciNet: MR2162421

Subjects:
Primary: 35K55
Secondary: 35B40

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 9 • 2005
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