The linear heat equation with highly oscillating potential

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KÖMBE İ.

Proceedings of the American Mathematical Society, cilt.132, sa.9, ss.2683-2691, 2004 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 132 Sayı: 9
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1090/s0002-9939-04-07392-7
  • Dergi Adı: Proceedings of the American Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2683-2691
  • Anahtar Kelimeler: Heat equation, Instantaneous blow up, Positive solutions
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

In this paper we consider the following initial value problem: ∂u/∂t = -Hu + V(x)u in ℝ N × (0,T), u(x,0)=u 0(x) ≥0 on ℝ N × {t=0}, where H = -Δ-β/|x| 2 sin(1/|x| α) and 0 ≥ V ∈ L loc 1 (ℝ N. Nonexistence of positive solutions is analyzed.