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 -convergence of solutions to a one-dimensional singular heat equation with -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}
}