The quenching behavior of a nonlinear parabolic equation with a singular boundary condition

ÖZALP N., Selcuk B.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.44, sa.3, ss.615-621, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 3
  • Basım Tarihi: 2015
  • Doi Numarası: 10.15672/hjms.2015449429
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.615-621
  • Anahtar Kelimeler: Nonlinear parabolic equation, singular boundary condition, quenching, quenching point, quenching time, maximum principles
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we study the quenching behavior of solution of a nonlinear parabolic equation with a singular boundary condition. We prove finite-time quenching for the solution. Further, we show that quenching occurs on the boundary under certain conditions. Furthermore, we show that the time derivative blows up at quenching point. Also, we get a lower solution and an upper bound for quenching time. Finally, we get a quenching rate and lower bounds for quenching time.