Periodic solutions for double degenerate quasilinear parabolic equations

✍ Scribed by Zhenhai Liu

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 124 KB
• Volume: 51
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00893-8

✦ Synopsis

on the space X = L 2 (0; T ; V ), where Q = ×(0; T ) and V = W 1; 2 0 (v; ) is a weighted Sobolev space, see Section 2. The degeneration is determined by a scalar function b(x) and a vector function v(x) = (v 1 (x); v 2 (x); : : : ; v N (x)) with positive components v i (x) in satisfying certain integrability assumptions.

Extensive attention has been paid to degenerate nonlinear parabolic equations by many authors in recent years, see, for example [3][4][5][6]8]. However, little information is known for this kind of double degenerate parabolic equations like (1.1). Only recently, Gan [3] studied the speciÿc degenerate parabolic equation @ @t (|x| u) -div(|x| * |Du| p-2 Du