Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics

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KITAVTSEV G., Taranets R. M.

Interfaces and Free Boundaries, cilt.22, sa.2, ss.157-174, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.4171/ifb/437
  • Dergi Adı: Interfaces and Free Boundaries
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.157-174
  • Anahtar Kelimeler: Porous medium, Singular heat, Viscous liquid sheets
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Orta Doğu Teknik Üniversitesi Kuzey Kıbrıs Kampüsü Adresli: Evet

Özet

In this paper, we extend the results of [8] by proving exponential asymptotic H1-convergence of solutions to a one-dimensional singular heat equation with L2-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory.