In this paper, we extend the results of  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.
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Georgy Kitavtsev, Roman M. Taranets, Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics. Interfaces Free Bound. 22 (2020), no. 2, pp. 157–174DOI 10.4171/IFB/437