Nonlinear degenerate parabolic equations for Baouendi-Grushin operators

KÖMBE İ.

Mathematische Nachrichten, cilt.279, sa.7, ss.756-773, 2006 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 279 Sayı: 7
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1002/mana.200310391
  • Dergi Adı: Mathematische Nachrichten
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.756-773
  • Anahtar Kelimeler: Baouendi-Grushin operator, Hardy inequality, Positive solutions
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

In this paper, we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equations: {∂u/∂t = Δγ (um) + V (z)u m in Ω × (0,t), 0 < m < 1 u(z,0) = u0(z) ≥0 in Ω, u(z,t) = 0 on ∂Ω × (0,T), and {∂u/∂t = ∇γ·(|∇γu| p-2 ∇γu) + V(z)up-1 in Ω × (0,T), 1 < p < 2, u(z,0) = u0(z) = u0 (z) ≥ 0 in Ω, u (z,t) = 0 on ∂Ω × (0,T) Here, Ω is a Carnot-Carathéodory metric ball in RN and V ε L loc1(Ω). The critical exponents m* and p*are found, and the nonexistence results are proved for m* ≤ m < 1 and p*≤ p < 2. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA.