Extinction and non-extinction for a p-Laplacian equation with nonlinear source

✍ Scribed by Ya Tian; Chunlai Mu

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 284 KB
• Volume: 69
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.08.021

✦ Synopsis

In this paper, we deal with the extinction of solutions of the initial-boundary value problem of the p-Laplacian equation u t = div(|∇u| p-2 ∇u) + λu q in a bounded domain of R N with N ≥ 2. For 1 < p < 2, we show that q = p -1 is the critical exponent of extinction for the weak solution. Furthermore, for 1 < p < 2 and q = p -1 we prove that the extinction and non-extinction of the solution depends strongly on the first eigenvalue of the problem -div(|∇φ| p-2 ∇φ) = λ|φ| p-2 φ, in Ω ; φ| ∂Ω = 0.