English

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

Analysis of PDEs 2018-10-05 v1

Abstract

In this paper, we extend the results of [1] by proving exponential asymptotic H1H^1-convergence of solutions to a one-dimensional singular heat equation with L2L^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.

Keywords

Cite

@article{arxiv.1810.02161,
  title  = {Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics},
  author = {Georgy Kitavtsev and Roman M. Taranets},
  journal= {arXiv preprint arXiv:1810.02161},
  year   = {2018}
}