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

Kitavtsev G., Taranets R. M.

INTERFACES AND FREE BOUNDARIES, cilt.22, sa.2, ss.157-174, 2020 (SCI-Expanded) identifier 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
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we extend the results of [8] by proving exponential asymptotic H-1-convergence of solutions to a one-dimensional singular heat equation with L-2-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.