Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains

✍ Scribed by Xianzhong Zeng

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 347 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.06.048

✦ Synopsis

This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that q c = n( p -1)/(np) is its critical exponent provided 2n/(n + 1) < p < n. Furthermore, we prove that if max{1, p -1} < q ≤ q c , then every positive solution of the equations blows up in finite time; whereas for q > q c , the equations admit the global positive solutions for some boundary value f (x) and some initial data u 0 (x). We also demonstrate that every positive solution of the equations blows up in finite time provided n ≤ p.