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.
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