Global Existence and Nonexistence in a System of Petrovsky

✍ Scribed by Salim A. Messaoudi

• Book ID: 102597730
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 110 KB
• Volume: 265
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7697

✦ Synopsis

In this paper we consider the nonlinearly damped semilinear Petrovsky equation

in a bounded domain, where a b > 0. We prove the existence of a local weak solution and show that this solution blows up in finite time if p > m and the energy is negative. We also show that the solution is global if m ≥ p.