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

Kitavtsev G., Taranets R. M.

INTERFACES AND FREE BOUNDARIES, vol.22, no.2, pp.157-174, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.4171/ifb/437
  • Journal Name: INTERFACES AND FREE BOUNDARIES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.157-174
  • Middle East Technical University Affiliated: Yes

Abstract

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.